FOXBOROUGH, Mass. – Alfonzo Dennard watched himself on the video board as he raced 87 yards with an interception for a touchdown. He wanted to see if the star rookie who threw the pass might catch him.

The way the New England Patriots were playing — with their usual strong offense, big plays on defense and a touchdown on a punt return — there was no way Andrew Luck and the Indianapolis Colts could overtake them.

The Patriots, the NFL’s highest-scoring team, equaled their single-game scoring record for points with a 59-24 win on Sunday.

“The coaches want us to play aggressive,” said Dennard, whose touchdown made it 45-17. “So that’s what I was doing out there.”

The first matchup between three-time Super Bowl winner Tom Brady and star rookie Luck was no match. Brady threw three touchdown passes. Luck threw three interceptions.

“They’re good enough,” Luck said. “They don’t need those gifts, but to their credit, they created those and we didn’t.”

The Patriots’ much-maligned pass defense finally made major contributions as newcomer Aqib Talib returned another interception for a touchdown, covering 59 yards. And Rob Ninkovich’s fifth forced fumble of the season — knocking the ball out of Luck’s hand — set up Rob Gronkowski’s second scoring grab on the next play.

“We knew we couldn’t come here and turn the football over and have a chance to win,” Colts interim coach Bruce Arians said. “We’ve got a lot of rookies out there so every week is a learning experience. It was a bad learning experience.”

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.

“I don’t think we’re anywhere (near) where we need to be at this point,” Brady said.

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 also scored on a 68-yard punt return by Julian Edelman three plays before Talib gave the Patriots the lead for good, 21-14.

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.

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. 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 on Talib’s touchdown to take the lead.

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 to the left, eluding numerous Colts.

Former Patriots kicker Adam Vinatieri, booed often in a stadium where he once was adored for his clutch three-pointers, cut the lead to 21-17 on a 47-yard field goal 5:46 before intermission.