Raiders quarterback Derek Carr, who threw three touchdown passes, left the game with 10:55 remaining in the fourth quarter after breaking his right fibula on a sack by Colts linebacker Trent Cole.
Carr was helped to the sideline and then carted to the locker room as backup Matt McGloin took over with the Raiders leading 33-14.
According to Raiders coach Jack Del Rio, Carr will have surgery, likely Sunday, and will be out indefinitely.
"It was a good win but a tough setback to have our quarterback go down like that," a somber Del Rio said. "Unfortunate. It's obviously is a blow. Teams have to find a way to pick up and move on. We'll rally around the next guy as best we can."
The Raiders (12-3), who clinched a playoff spot last week for the first time since 2002, moved 1 1/2 games ahead of the Kansas City Chiefs (10-4) in the AFC West. The first-place Raiders can win the West and secure a first-round playoff bye on Sunday if the Chiefs lose to the Denver Broncos or that game ends in a tie.
Carr has already been ruled out for Oakland's regular-season finale at Denver, but Del Rio said he didn't know whether he'll have a chance to return at any point in the playoffs.
"Everybody heals differently," Del Rio said. "We'll see exactly what needs to be done when they get in there and do it. ... I think he's going to be down a little while."
The Colts (7-8) were eliminated from playoff contention and will miss the postseason for the second straight season.
"You work hard all year for opportunities like this, to be able to get to the dance and see what happens after that," Colts running back Robert Turbin said. "But to not be in it this year is definitely disappointing, and it hurts. But that's the league. That's life. It's hard."
Rookie running back DeAndre Washington ran for 99 yards and two scores on 12 carries for the Raiders, who had 210 net rushing yards.
Carr, an MVP contender, completed 20 of 30 passes for 228 yards. He has thrown for 3,933 yards and 28 touchdowns with six interceptions. McGloin completed 2 of 3 passes for 29 yards, including a 19-yard throw to wide receiver Amari Cooper to ice the victory.
"It's a difficult situation because first and foremost he's a very good friend of mine," McGloin said. "It's tough to see him go down and him get hurt in a situation like that. He's been having such an incredible season for himself, and to see him go down like that was tough. But at the same time I did my best to try to stay calm, stay focused and do my job out there."
Raiders wide receiver Michael Crabtree caught seven passes for 90 yards.
Colts quarterback Andrew Luck completed 19 of 29 passes for 288 yards and two touchdowns with two interceptions. Frank Gore rushed for 73 yards on 13 carries, and T.Y. Hilton caught four passes for 105 yards.
"Obviously, we're all very disappointed," Colts coach Chuck Pagano said. "We had numerous opportunities and numerous chances. It's hard. Football's hard."
The Raiders built a 19-7 halftime lead as Carr threw for 163 yards and three touchdown passes and safeties Nate Allen and Reggie Nelson each intercepted a Luck pass.
Carr's 1-yard touchdown pass to wide receiver Andre Holmes put Oakland ahead 7-0 with 14:57 left in the first half.
Luck answered with a 24-yard touchdown pass to wide receiver Donte Moncrief with 9:49 left in the half.
Oakland marched 79 yards in eight plays for Carr's 5-yard touchdown pass to tight end Clive Walford. Sebastian Janikowski missed the extra point attempt, leaving the Raiders lead at 13-7 with 5:50 remaining.
Indianapolis quickly moved to the Raiders' 29-yard line, but on second-and-10, Nelson cut in front of Hilton in the right front corner of the end zone and intercepted Luck's pass.
Carr marched the Raiders 80 yards in six plays for a touchdown as running back Jalen Richard scored on a 4-yard screen pass with 18 seconds showing. Janikowski missed the point-after attempt again, marking the first time in his career he botched back-to-back extra points.
Oakland took the second-half opening kickoff and went 77 yards on seven plays with Washington scoring on a 22-yard run. Janikowski's PAT was good, increasing the Raiders' lead to 26-7 with 10:48 left in the third quarter.
On the Colts' ensuing drive, linebacker Malcolm Smith forced a fumble by Gore and cornerback TJ Carrie recovered at the Colts' 38. Three plays later, Washington sliced over right guard and raced 22 yards for a touchdown, increasing Oakland's lead to 33-7 with 8:40 left in the third quarter.
Indianapolis cut the Raiders' lead to 33-14 on Luck's 3-yard touchdown pass to running back Robert Turbin with 5:18 remaining in the third.
The Colts pulled closer at 33-22 on Luck's 11-yard touchdown run and two-point pass to Hilton with 7:40 left.
NOTES: Colts CB Darius Butler sustained a concussion midway through the second quarter and did not return. ... Raiders QB Derek Carr took a few snaps under center for first time since Nov. 27 against Carolina when he dislocated his right pinky finger. ... Raiders DE Mario Edwards Jr. (hip) made his season debut after missing the first 14 games while on injured reserve-designated for return. He was activated Friday. ... Raiders RT Austin Howard was inactive, and Menelik Watson started in his place. ... Colts DT Henry Anderson made his first start of the season, replacing NT Zach Kerr.