FOXBOROUGH, Mass. -- Rob Gronkowski scored three more touchdowns. Chances are the New England Patriots are thinking more about the three touchdowns they allowed in the fourth quarter.

Against the winless Colts, no less.

The Patriots needed Deion Branch to recover an onside kick in the final minute to hold off Indianapolis 31-24 on Sunday. Trailing 31-3, the Colts rallied with a touchdown run by Donald Brown and two scoring passes from Dan Orlovsky to Pierre Garcon, the last with 36 seconds to go.

Tom Brady took a knee on the final play to complete the victory.

"We played good for 45 minutes and then didn't do anything offensively," Brady said. "So we'll hear about that."

The Patriots (9-3) have won four straight and are tied for the AFC's best record. Indianapolis (0-12) must beat Baltimore, Tennessee, Houston or Jacksonville to avoid becoming the second NFL team to go 0-16.

"People can say what they want to say about not playing hard, but I think that (comeback) pretty much shut that up right there," Colts tight end Jacob Tamme said.

With two touchdowns passing, both to Gronkowski, Brady overtook Johnny Unitas and tied Warren Moon for sixth place in NFL history with 291 during the regular season. Brady was 29 of 38 for 293 yards.

Gronkowski has 13 touchdown catches, tying San Diego's Antonio Gates in 2004 and San Francisco's Vernon Davis in 2009 for most by a tight end in a regular season. He originally was given another touchdown catch, but that was changed to a lateral on which he ran 2 yards for the 31-3 lead.

Thinking he had set the record, Gronkowski held onto the ball as a souvenir instead of spiking it as he usually does. He even accepted congratulations from his teammates.

"I wasn't thinking about whether it was a pass or a lateral," Gronkowski said. "I'll take the rushing touchdown. It's the first of my whole career."

The Patriots entered the game as three-touchdown favorites with the teams, from different divisions, meeting for the ninth straight season.

"Guys played well and did some things well," Colts coach Jim Caldwell said, "but, still, we're measured by wins."

Caldwell gave Orlovsky his first start of the season in place of the ineffective Curtis Painter. Orlovsky, a member of the winless Detroit Lions team in 2008, completed 30 of 37 for 353 yards, two touchdowns and one interception.

"We felt confident going into the game that if we stayed patient we could move the ball," Orlovsky said. "We fell short. I wish we had more time on the clock."

Watching from the sideline was Peyton Manning, whose preseason neck surgery forced Caldwell to go with backups.

"We almost had a big win today. It would have been huge for us," Manning said.

The Colts tied the score 3-3 on Adam Vinatieri's 31-yard field goal early in the second quarter. And the Patriots punted on their next series.

Then Brady got the offense rolling as New England scored touchdowns on its next four possessions, taking a 31-3 lead late in the third quarter. Wes Welker caught 11 passes for 114 yards, increasing his NFL-leading total to 93 receptions.

The Colts had a new defensive coordinator, linebackers coach Mike Murphy, after Larry Coyer was fired Tuesday.

The Patriots rarely lose in December, no matter their opponent. They're 38-5 in that month starting in 2001, tops in the NFL. And they're 19-1 at home in December, with wins in their last 18 games, since Gillette Stadium opened in December 2002.

Trailing 3-0, Orlovsky led a 19-play drive lasting 10:19. The Colts had first-and-goal at the one, but a run for no gain, an incompletion, a false-start penalty and a sack forced them to settle for Vinatieri's field goal.

New England took command by scoring twice in the last three minutes of the first half on Brady's 11-yard pass to Gronkowski and BenJarvus Green-Ellis' 1-yard run for a 17-3 lead.

The Patriots got the ball to start the third quarter and Brady passed on each of the seven plays, completing all of them to drive 77 yards, ending with a 21-yard touchdown to Gronkowski. After a fumble recovery, Gronkowski scored again when he went in motion, took a toss from Brady and ran untouched into the right side of the end zone.

"He is a tough kid and he knows how to run the routes," Colts defensive back Jerraud Powers said. "It also helps when you have one of the greatest quarterbacks."

Gronkowski finished with five catches for 64 yards after entering the game tied for sixth in the NFL with 60 receptions.

The Colts scored in the fourth quarter on Donald Brown's 5-yard run and Orlovsky's passes of 33 and 12 yards to Garcon.

"If we don't play four quarters, we're not going to end up in the situation we want to be in," Welker said.

The Patriots want to win the Super Bowl. The Colts have a more modest goal -- winning just one game.

"I thought Dan was patient," Manning said. "I really thought he did a good job. He gave us a chance there at the end."

And Orlovsky gave Patriots coach Bill Belichick something to harp on when he meets with his players.

"We've obviously got to do a better job of finishing the game," Belichick said. "That was disappointing, but we'll work on that."

Notes: Brady has thrown for 30 touchdowns, becoming the sixth player in NFL history to do that at least three times. ... The Colts outgained the Patriots 437 yards to 366. ... The Patriots clinched a winning record for the 11th straight season.