The Heat are just the second eighth seed to reach the N.B.A. championship series. They beat Boston, the No. 2 seed, in the Eastern Conference finals.The Miami Heat stunned the Boston Celtics in the Eastern Conference finals on Monday night, clinching a roller-coaster, hold-your-breath, best-of-seven series in Game 7, 103-84, to extend their remarkable postseason run.“I had so much belief in myself and this group of guys,” said Heat forward Jimmy Butler, who was named the most valuable player of the series. He scored 28 points in Game 7.The Heat, whose resurgence as the East’s No. 8 seed has seemingly surprised everyone but them, will face the Denver Nuggets in the N.B.A. finals beginning Thursday. The Nuggets secured their first trip to the championship round by completing a sweep of the Los Angeles Lakers in the Western Conference finals a week ago. The Heat are just the second eighth seed, after the 1998-99 Knicks, to reach the N.B.A. finals under the current playoff format.Not that it was easy. “Sometimes you have to suffer for the things you really want,” Heat Coach Erik Spoelstra said during the postgame trophy presentation.After the Heat won the first three games of the series, the Celtics regained their rhythm and won the next three to force a seventh and deciding game at home. Boston was bidding to become the first team to win an N.B.A. playoff series after trailing, 3-0. But Miami avoided becoming a historical footnote/punchline by dipping into its bottomless well of perseverance.Even when the Heat were scuffling in the regular season, losing nearly as often as they won, Spoelstra stuck with his approach.Miami Heat forward Jimmy Butler struggled in the second half of the series but came through in Game 7.Maddie Meyer/Getty ImagesSpoelstra said he sensed that the Heat were capable of improving if they continued to focus on their daily work. There was nothing especially sexy about it — meeting after frustrating losses, watching film, practicing hard.“Those are gratifying experiences,” Spoelstra said earlier in the series, “particularly when you’re losing games and you’re getting criticized for it. But you’re still able to just come together and try to get it right.”The Heat went about six months without getting it right. But over the past six weeks, they have unlocked all their promise and potential to clinch another appearance in the N.B.A. finals. It is the franchise’s seventh in its 35 seasons and second in the past four years.“The ups and downs prepared us for these moments,” Bam Adebayo, the Heat’s All-Star center, said during the series as the Heat went about their business of outlasting the Celtics.The Heat won the first two games of the series in Boston then routed the Celtics in Miami in Game 3. Spoelstra said “a lot of pent-up stuff” had been fueling his team but declined to elaborate.His players were more forthcoming: They recalled being eliminated by the Celtics in the conference finals last season, an especially disappointing exit since the Heat were the East’s top seed and the series went seven games.The Heat nearly blew it this time around. Before Game 7, the Celtics were entertaining dreams of replicating the Boston Red Sox’s dramatic comeback in the 2004 American League Championship Series, when they made baseball history by coming back from a 3-0 series deficit to eliminate the Yankees. The Red Sox then swept the St. Louis Cardinals in the World Series to win their first championship since 1918.But Miami was too determined and too tough, finding beauty in the struggle. Butler, the team’s gifted two-way forward, imposed his will early in the series, while Adebayo was a defensive menace. But their supporting cast made the difference.Caleb Martin, a small forward who moved into the starting lineup for Games 6 and 7, was the Heat’s most consistent player throughout the series. He had 26 points in Game 7 and made of 11 of his 16 shots, including four 3-pointers. Gabe Vincent, the team’s starting point guard, played the final two games with a sprained ankle. And Duncan Robinson came off the bench to make timely 3-pointers.On Monday, before a hostile crowd that was at a fever pitch during player introductions, the Heat seemed intent on drowning out the noise by relying on their defense. The Celtics missed all 10 of their 3-point attempts in the first quarter; in the second quarter, the Heat led by as many as 17 points.Boston had cut into Miami’s lead when Martin went to work again, closing the third quarter with a turnaround baseline jumper. He opened the fourth quarter with his fourth 3-pointer of the game, and the Heat’s lead was back to 13.Adebayo had been asked earlier in the series about the key to the team’s success.“Believing,” he said. “Believing in one another. Believing that we can get a win. Believing that we can beat the No. 1 team in the league. You know, belief is real, and we’ve got a will to win.”The Heat did indeed beat the No. 1 team, upsetting the Milwaukee Bucks, who had the league’s best regular-season record, in the first round of the playoffs. They beat the fifth-seeded Knicks in six games in the second round to set up their series with Boston.The Celtics figured to make another deep playoff run after losing to the Golden State Warriors in the N.B.A. finals last season. But obstacles — both predictable and unforeseen — hindered them before they even convened for the preseason.Atop the list was the sudden absence of Ime Udoka, who, as the Celtics’ first-year head coach last season, left his defense-minded imprint on the team. But in September, less than a week before training camp, the Celtics suspended him for the season for “violations of team policies.” Two people briefed on the matter, who were not authorized to speak about it publicly, said Udoka had a relationship with a female subordinate.Boston’s Jaylen Brown struggled in Game 2, hitting just one 3-pointer in seven attempts.Adam Glanzman/Getty ImagesBoston’s Jayson Tatum scored just 14 points in a blowout loss to Miami in Game 3.Wilfredo Lee/Associated PressThe entire situation cast an unwelcome shadow on the Celtics as they sought to focus on the season ahead. “It’s been hell,” Marcus Smart, the team’s starting point guard and last season’s defensive player of the year, said at the time.Instead of going outside the organization to hire an experienced coach as Udoka’s replacement, the team prioritized continuity by temporarily promoting Joe Mazzulla, who had been an assistant on Udoka’s staff.Mazzulla, 34, whose only previous head coaching experience was at Fairmont State, a Division II program in West Virginia, had suddenly been placed in charge of an N.B.A. team with championship expectations. It was a gamble that appeared to be paying off by the All-Star break, when Boston had the league’s best record. The Celtics named Mazzulla as their permanent head coach in February and officially severed ties with Udoka, whom the Houston Rockets hired as head coach last month.But Boston slumped over the final weeks of the regular season, slipping to the No. 2 seed in the East behind Milwaukee, and needed six games to eliminate the Atlanta Hawks in the first round. (The series went so unexpectedly long that Janet Jackson had to postpone a concert in Atlanta. Boston’s Jayson Tatum publicly apologized to her.)The pressure only mounted on Mazzulla — and on the team’s two stars, Tatum and Jaylen Brown — during the Celtics’ conference semifinal matchup with the Philadelphia 76ers. Tatum and Brown were inconsistent as the series stretched to seven games. Mazzulla was scrutinized for some of his lineup choices and for his apparent aversion to calling timeouts in critical situations.“Joe’s learning, just like all of us,” Smart said during the series. “I know he’s been killed a lot, rightfully so.”But after Tatum scored 51 points in a series-clinching tour de force against the 76ers, the Celtics ran into the Heat, a savvy and experienced opponent with payback in mind.In the postseason, Miami’s Jimmy Butler has become known for morphing into “Playoff Jimmy” — a better version of himself.Adam Glanzman/Getty ImagesThe Heat traveled a long, hard road merely to reach the conference finals. They had to defeat the Chicago Bulls in a play-in game to slip into the postseason. They proceeded to lose two rotation players, Tyler Herro and Victor Oladipo, to injuries in their first-round series with the Bucks.But the Heat were not about to let up against the Celtics — not after a season of growth under Spoelstra, not with Butler filling his more unsung teammates with confidence, and not against an opponent that had buried Miami’s championship dream a year ago.“We go out there and we hoop and we play basketball the right way,” Butler said, “knowing that we’ve always got a chance.” More