PITTSBURGH — Ben Roethlisberger shook off a knee injury and threw for 220 yards and a touchdown as the Pittsburgh Steelers clinched a playoff berth with a 20-12 victory over the Kansas City Chiefs on Sunday.

The veteran quarterback completed 18 of 25 passes in helping the Steelers (10-5) to their third straight win. They are headed to the playoffs for the first time since 2011 following back-to-back 8-8 seasons.

The Steelers can win the AFC Central title next Sunday when they host the Cincinnati Bengals (9-4-1) in the regular-season finale.

The Chiefs (8-7) had their playoff hopes severely damaged while losing for the fourth time in their last five games. Kansas City has to beat San Diego Chargers at home next Sunday and also hope for help from other teams in order to reach the postseason.

Though quarterback Alex Smith had his first 300-yard passing game since 2012 — finishing with 311 — all of the Chiefs’ points came on four field goals by rookie kicker Cairo Santos.

Roethlisberger injured his right knee when hit while throwing a 3-yard touchdown pass to wide receiver Antonio Brown that gave the Steelers a 17-6 lead with 34 seconds remaining in the third quarter.

Roethlisberger was taken to the locker room for examination by the team’s medical staff while backup quarterback Bruce Gradkowski began warming up. However, Roethlisberger quickly returned to the sidelines and went back into the game when the Steelers regained possession following a 43-yard field goal by Santos with 10:18 left that drew the Chiefs within eight points.

Roethlisberger then led the Steelers on a 12-play, 70-yard drive that culminated in a 23-yard field goal by kicker Shaun Suisham with 4:04 to go that increased their lead to 20-9.

Santos’ fourth field goal, a 23-yarder with 1:37 left, cut the Steelers’ lead to eight again but Pittsburgh recovered an onside kick and ran out the clock.

Neither the Steelers’ Le’Veon Bell nor the Chiefs’ Jamaal Charles stood out in a matchup of two of the NFL’s top running back. Bell rushed for 63 yards on 20 carries and Charles had 29 yards on nine attempts.

Brown had seven receptions for 72 yards and Pittsburgh tight end Heath Miller added seven catches for 68 yards.

Bell’s 1-yard touchdown with 4:18 left in the second quarter finished an 11-play, 80-yard drive and gave the Steelers a 10-6 halftime lead. Pittsburgh’s defense stopped the Chiefs on downs at the Steelers’ 12 with 20 seconds left

Until Bell’s touchdown, all the scoring had come on field goals as Santos hit from 35 and 25 yards and Suisham connected from 23.

NOTES: Steelers WR Antonio Brown broke his own franchise single-season record for receiving yards by bringing his total to 1,569. He had 1,499 last season. Brown’s 122 receptions are also a team record. … Steelers SS Troy Polamalu (knee) sat out and S Will Allen took his spot in the starting lineup. … Pittsburgh LB James Harrison returned to action after missing the previous two games with a knee injury. … Chiefs WR Donnie Avery was an inactive despite not being on the injury report during the week. Avery, who has played only once since Week 4, has a lingering groin injury. … Kansas City WR Dwayne Bowe (illness) started despite not being able to practice all week.