Rob Gronkowski scored three more touchdowns, and turned out the Patriots needed every one of them to keep Indianapolis winless.
New England withstood the Colts' three-touchdown rally in the fourth quarter for a 31-24 victory Sunday.
The Patriots (9-3) have won four in a row. Indianapolis (0-12) must beat Baltimore, Tennessee, Houston or Jacksonville to avoid becoming the second NFL team to go 0-16.
Trailing 31-3, the Colts rallied with a touchdown run by Donald Brown and scoring passes of 33 and 40 yards from Dan Orlovsky to Pierre Garcon, the last with 36 seconds to go. But Deion Branch recovered the onside kick and Tom Brady took a knee on the final play.
The Patriots entered the game as three-touchdown favorites with the teams, from different divisions, meeting for the ninth straight season.
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 completed 29 of 38 for 293 yards.
Colts coach Jim Caldwell gave Orlovsky his first start of the season in place of the ineffective Curtis Painter. Orlovsky, a member of that winless Lions team, completed 30 of 37 passes for 353 yards, two touchdowns and one interception.
Watching from the sideline was Peyton Manning, whose neck surgery before the season forced Caldwell to go with those backups.
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.
The Colts had a new defensive coordinator, linebackers coach Mike Murphy, after Larry Coyer was fired Tuesday.
But 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.
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 on the bench.
Trailing 3-0, Orlovsky led a 19-play drive lasting 10:19. The Colts had first-and-goal at the 1, 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 finally 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 Kyle Arrington recovered Delone Carter's fumble on the next series, Gronkowski scored again when he went in motion, took a pitch from Brady and ran untouched into the right side of the end zone.
This program aired on December 4, 2011. The audio for this program is not available.