The Patriots (7-3) won their fourth straight game and extended their lead in the AFC East to three games over the other three teams. The Colts (6-4) had their four-game winning streak stopped by the NFL's best offense and one of its worst defenses.
Now New England must hurry to prepare for its Thanksgiving night meeting with the Jets (4-6). New York ended a three-game slide with a 27-13 win over the St. Louis Rams.
For the Patriots, Sunday's win was their most complete in a season in which they've averaged 35.8 points per game and lost their three games by a combined margin of four points.
The 59 points equals the team mark set in a 59-0 win over the Tennessee Titans on Oct. 18, 2009.
The Patriots scored on a 68-yard punt return by Julian Edelman and on interception returns of 59 yards by newcomer Aqib Talib and 87 yards by Alfonzo Dennard. And Rob Ninkovich's fifth forced fumble of the season set up Rob Gronkowski's second scoring grab on the next play.
Brady completed 24 of 35 passes for 331 yards and no interceptions. Luck was 27 for 50 for two touchdowns and 334 yards and set an NFL record as the first rookie with five 300-yard games. But he also threw three interceptions.
The Colts were competitive for one half. The Patriots led 24-17 heading into the third quarter.
Then the Patriots scored on passes of 2 yards to Edelman and 24 yards to Gronkowski and Dennard's interception return.
Luck followed with a 43-yard scoring pass to T.Y. Hilton, the second of the game to the fellow rookie, But the Patriots responded with touchdown runs of 3 yards by Stevan Ridley and 4 yards by Shane Vereen.
The game began with touchdowns on the first three series a 1-yard run by Delone Carter of the Colts, a 4-yard pass from Brady to Gronkowski, and a 14-yard pass from Luck to Hilton.
Stephen Gostkowski then missed a 36-yard field goal attempt for the Patriots.
But their fortunes changed four plays later when Edelman brought a punt back for a touchdown for the third time in his career after the defense forced Luck into a three-and-out. And just three plays and 61 seconds after that, the Patriots scored again on Talib's touchdown as the Patriots took the lead for good 21-14 with 10:59 left in the second quarter.
The catch was an easy one Luck threw the ball high over Reggie Wayne's head but the run was exceptional as Talib cut from the right side of the field all the way to the left, eluding numerous Colts.
The Patriots obtained Talib from Tampa Bay before last Sunday's 37-31 win over Buffalo. But he sat that one out to complete a four-game suspension for violating the NFL policy on performance-enhancing substances.
Former Patriots kicker Adam Vinatieri, booed often in a stadium where he once was adored, cut the lead to 21-17 on a 47-yard field goal 5:46 before intermission.
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Indianapolis 24, New England 59
Indianapolis 14 3 0 7 24
New England 7 17 14 21 59
Ind • Carter 1 run (Vinatieri kick), 10:49.
NE • Gronkowski 4 pass from Brady (Gostkowski kick), 7:07.
Ind • Hilton 14 pass from Luck (Vinatieri kick), 1:44.
NE • Edelman 68 punt return (Gostkowski kick), 12:00.
NE • Talib 59 interception return (Gostkowski kick), 10:59.
Ind • FG Vinatieri 47, 5:46.
NE • FG Gostkowski 31, 1:54.
NE • Edelman 2 pass from Brady (Gostkowski kick), 11:07.
NE • Gronkowski 24 pass from Brady (Gostkowski kick), 3:22.
NE • Dennard 87 interception return (Gostkowski kick), 14:47.
Ind • Hilton 43 pass from Luck (Vinatieri kick), 12:32.
NE • Ridley 3 run (Gostkowski kick), 9:05.
NE • Vereen 4 run (Gostkowski kick), 3:55.
Attendance • 68,756.
First downs 28 25
Total Net Yards 448 446
Rushes-yards 24-119 25-115
Passing 329 331
Punt Returns 1-7 2-117
Kickoff Returns 7-104 4-94
Interceptions Ret. 0-0 3-166
Comp-Att-Int 27-50-3 24-35-0
Sacked-Yards Lost 1-5 0-0
Punts 3-46.3 2-57.0
Fumbles-Lost 3-1 1-0
Penalties-yards 1-5 4-70
Time of Possession 32:55 27:05
Rushing • Indianapolis, Ballard 16-72, Carter 2-21, D.Brown 4-17, R.Hughes 1-5, Luck 1-4. New England, Edelman 1-47, Vereen 11-40, Ridley 13-28.
Passing • Indianapolis, Luck 27-50-3-334. New England, Brady 24-35-0-331.
Receiving • Indianapolis, Wayne 7-72, Hilton 6-100, Allen 6-69, Avery 3-34, Brazill 2-46, D.Brown 2-6, Ballard 1-7. New England, Gronkowski 7-137, Welker 7-80, Edelman 5-58, Lloyd 4-45, Vereen 1-11.
Missed Field Goals • Indianapolis, Vinatieri 58 (WL). New England, Gostkowski 36 (WR).