NEW YORK — The New England Patriots are back in the hunt for the AFC championship and the No. 4 seed in the AFC playoff race after defeating the Indianapolis Colts 34-23 in overtime on Sunday night to keep their playoff hopes alive.

The Patriots (6-2) have won three of their last four games and are on a three-game winning streak.

Quarterback Tom Brady was a game-winner in the fourth quarter, giving the Patriots a 35-34 victory that extended New England’s lead over the Indianapolis (5-4) to 3-0.

New England had its first lead at 24-0 with 6:56 left, but Colts quarterback Andrew Luck threw an interception and was sacked for a loss of nine yards.

Luck threw for 329 yards and two touchdowns, but he also threw three interceptions, was sacked six times and fumbled twice.

The Colts (4-5) trailed 26-17 midway through the fourth but rallied to get within a score with 2:15 left.

But Brady missed a 47-yard field goal that would have given the Patriots the win.

He threw three touchdown passes to tight end Logan Paulsen and running back Coby Fleener and also caught a pass from running back LeGarrette Blount.

Fleener ran for 93 yards and a touchdown and scored on a 4-yard run to make it a 24-24 game with 8:18 left.

The Patriots were missing a key player, linebacker Jamie Collins, who is out for at least the first four weeks with a hamstring injury.

The NFL’s official injury report lists Collins, linebacker Vince Wilfork, tight end Rob Gronkowski and cornerback Kyle Arrington as probable for Sunday’s game against the Colts.

New Orleans Saints quarterback Drew Brees and running backs Adrian Peterson and Alvin Kamara also missed the game because of injuries.