Cleveland Browns fans love to revel in their misery. The long list of dud coaches. The unending line of quarterback busts. The team abandoning the city only to return a few years later. And all that losing, including a winless season in 2017.

But Browns Nation got some measure of payback on Sunday when the Browns beat their rivals, the Pittsburgh Steelers, 24-22, in the regular-season finale, and qualified for the N.F.L. playoffs for the first time since the 2002 season, an absence of 17 years.

The two teams — the Steelers (12-4), as the third seed in the A.F.C., and the Browns (11-5), as the sixth — will meet again next week in Pittsburgh in the wild-card round.

The Browns’ victory ended the longest playoff drought in the N.F.L. (the Jets now take over the top spot with a 10-year absence) and completed a makeover that began three years ago when Cleveland chose quarterback Baker Mayfield as the first overall pick in the draft.

When asked about what the victory meant to the team’s fans, Mayfield said, “It means so much to this city.”

The win, in front of a pandemic-limited crowd of about 12,000 fans at FirstEnergy Stadium in Cleveland, provided an extra dose of satisfaction because it came against the Steelers, who have dominated the Browns for decades. Since the Steelers beat the Browns in the wild-card round in January 2003 — Cleveland’s last postseason appearance — Pittsburgh has won 29 of their 36 matchups.

During that fallow period, the Browns have burned through 25 quarterbacks, 10 head coaches and a whole lot of hope. The team has gone 91-196 since its last playoff appearance (a .317 winning percentage), a stretch that has included 14 seasons with double-digit losses. Their only winning season during that stretch had been in 2007, when the Browns were 10-6.

The Steelers had clinched the A.F.C. North and had no way to claim the top seed in the A.F.C. and its first-round bye, so they sat several of their best players on Sunday, including quarterback Ben Roethlisberger.

The Browns were short-handed as well. Six players were on the Covid-19 list and several offensive linemen were injured. Cleveland went without any starting wide receivers last week in a loss to the Jets because of an outbreak on the team. Several more players and coaches were added to the Covid list since then.

This made the challenge bigger for the Browns, even though they were playing at home and against the Steelers’ backup quarterback, Mason Rudolph.

The Browns opened with a bang, scoring a touchdown and field goal on their first three possessions, sparked in part by running back Nick Chubb, who passed 1,000 yards rushing for the season.

But the Steelers kept the game close with three field goals through three quarters. The Browns, though, found a way to stay one step ahead.

After Pittsburgh narrowed the score to 10-9, Mayfield scrambled for 28 yards to keep the next drive alive. He then hit tight end Austin Hooper with a 2-yard touchdown pass to put the Browns up, 17-9.

On the ensuing drive, M.J. Stewart of the Browns intercepted Rudolph and returned the ball to the Pittsburgh 20-yard line. Wide receiver Jarvis Landry ran for a touchdown four plays later to push the lead to 24-9.

No Browns win over the Steelers comes easily. Rudolph hit wide receiver Chase Claypool for a 28-yard score. On the next drive, the Steelers sacked Mayfield to push the Browns out of field-goal range. They then failed to convert a fourth-down play, which gave the Steelers the ball back with 3 minutes 35 seconds to play.

Rudolph hit wide receiver Diontae Johnson for a 47-yard completion, then threw a touchdown to JuJu Smith-Schuster to narrow the score to 24-22.

The Browns broke up the 2-point conversion to maintain the lead, but nearly fumbled the recovery on an onside kick. It wasn’t until Mayfield ran 3 yards for a first down that the Browns were able to run out the clock, secure the win and punch their ticket to the postseason.