The Cleveland Browns’ postseason drought grew from a crabby and cranky toddler into an exasperating adolescent. After its tumultuous teens, it seems ready to say goodbye.

The Browns are primed to qualify for the playoffs for the first time in 18 years after bludgeoning the Tennessee Titans on Sunday, a 41-35 victory in Nashville that improved their security in the standings to an extent largely alien in northeast Ohio since the current incarnation of the franchise returned in 1999. Only twice before in that span had Cleveland finished with even a nonlosing record, but the Browns are now 9-3 for the first time since 1994, when they won their last playoff game and Bill Belichick prowled their sideline.

It’s unclear whatever happened to that guy, but the Browns, in the meantime, endured one self-inflicted indignity after another: from a relocation to Baltimore to numerous regime changes to a 1-31 stretch that produced the draft capital that has spurred this revival. The Browns’ top offensive selections from their critical 2018 draft — quarterback Baker Mayfield, taken first over all, and running back Nick Chubb, chosen in the second round — contributed to all five touchdowns against the Titans (8-4) on Sunday, each coming in the dizzying first half, which produced a most improbable halftime score of Cleveland 38, Tennessee 7.

“I think people know that we are a good team now,” Chubb said.

This game represented a pivot point in Cleveland’s season, at once an opportunity to dismiss a perception that it had puffed its record with victories against inferior teams and to affirm it is levelheaded enough to defeat another A.F.C. contender. In a matchup of 8-3 teams with powerful rushing offenses — Cleveland ranked first in the N.F.L., Tennessee second — both strayed from type.

The Titans, who had five turnovers all season, committed three on Sunday. And the Browns, echoing the aggressive approach they deployed in scoring 49 points at Dallas earlier this season, called trick plays and passed often, sprinkling in Chubb and his dynamic backfield counterpart, Kareem Hunt, instead of relying on them. The play design and play-calling of Coach Kevin Stefanski, coupled with Mayfield’s execution, generated one touchdown pass after another — a dart to Jarvis Landry, a goal-line grab by offensive lineman Kendall Lamm, a deep ball off a nifty play fake to Donovan Peoples-Jones, a lofted toss to Rashard Higgins. At halftime, Mayfield had completed 21 of 26 passes for 296 of his 334 yards.

“He’s playing at a high level and he has to continue to do so,” Stefanski said. “We’re counting on him, and he knows that.”

In a game that featured 76 total points and 889 total yards, it was two defensive plays that truly powered the Browns. Those plays countered consecutive first-quarter carries by Derrick Henry, who seemed to embark on his annual December rampage last week when he rushed for 178 yards and three touchdowns against Indianapolis. On Sunday, Cleveland stuffed Henry, among the league’s best short-yardage backs, on fourth-and-1, then stripped him deep in Tennessee territory. The Browns’ 3-0 lead ballooned to 17-0. Had the Titans’ Mike Vrabel coached beneath a ladder while a black cat circled his feet, the first half couldn’t have gone worse for Tennessee.

The Browns’ minus-15 point differential is the worst for a team that has won at least nine of its first 12 games in N.F.L. history, according to the Elias Sports Bureau. With occasional exceptions — Houston (minus-7) last season, Buffalo (minus-57) and Tennessee (minus-22) in 2017 — teams with negative point differentials don’t reach the playoffs because teams with negative point differentials generally don’t win that often.

The Browns had won their last three games by a combined 10 points, but for them the margin was irrelevant. They are winning games by minimizing mistakes — Mayfield fumbled late Sunday, but he hasn’t thrown an interception since Oct. 25 — and recognizing their strengths.

The playoff hype that reached a zenith before the 2019 season, when an influx of talent raised expectations to an unhealthy degree, is more legitimate now that Cleveland, under Stefanski and the new general manager, Andrew Berry, is rooted in stability.

“They need to reset their expectations,” Mayfield said, referring to Browns fans. “We all need to reset the standard, and that’s what I’ve been saying. There’s a new standard, there’s a foundation we have to continue to build on and improve. That’s just the way we need to handle things.”

With four games remaining, Cleveland holds the top wild-card spot in the A.F.C., a game ahead of Miami and Indianapolis (both 8-4), which currently have the other two postseason berths, and two games ahead of Las Vegas (7-5). The division rival Baltimore (6-5), Cleveland’s opponent next Monday night, and New England (6-6) are also in the mix.

If all goes as scheduled, the Browns’ season will end at home against unbeaten Pittsburgh on Jan. 3, two days short of the 18th anniversary of their last playoff game and a fine day to bid it farewell.