FOXBOROUGH, Mass.—  The Tom Brady-Rob Gronkowski connection kept clicking. The New England Patriots’ defense and special teams kept rolling, too.

Brady threw two touchdown passes to Gronkowski, Julian Edelman returned a punt 72 yards for another score and Kyle Arrington had two interceptions to help the Patriots beat the Kansas City Chiefs 34-3 on Monday night.

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Julian Edelman returns a punt 72 yards for a touchdown Monday night in the Patriots’ 34-3 win over the Kansas City Chiefs at Gillette Stadium. The Associated Press

The Patriots (7-3) increased their AFC East lead to two games.

The Chiefs (4-6) weren’t expected to do much on offense behind untested quarterback Tyler Palko, making his first career start with Matt Cassel injured. And they didn’t, managing just a 26-yard field goal by Ryan Succop with 1:30 left in the first quarter for their only lead.

With Gronkowski collecting his ninth and 10th TD receptions of the year, the Patriots had their second straight dominant game after beating the New York Jets 37-16. The Chiefs lost their third straight.

The Patriots didn’t generate much of an attack during their first four series. There were three punts and a fumble by Brady that was recovered by Kansas City’s Allen Bailey on the first play of the second quarter. And on his next series, Brady was sacked twice.

Then the protection improved and Brady, who had thrown for just 19 yards in the first quarter, took advantage, leading three consecutive scoring drives.

He connected with Gronkowski for a 52-yard score in which the tight end caught the ball over the middle and scampered the last 35 yards, barely managing to remain inbounds on the right side as he neared the end zone.

Arrington, who leads the NFL with seven interceptions, got his first of the game on Kansas City’s next series and Stephen Gostkowski made it 10-3 at halftime with a 21-yard field goal.

The Patriots got the ball to start the third quarter and marched 85 yards on nine plays, scoring on Brady’s 19-yard pass to Gronkowski, who somersaulted into the right corner of the end zone after being hit by Derrick Johnson.

Gronkowski has 20 touchdowns in 26 games, surpassing Mike Ditka’s mark of 31 for the fewest games needed by a tight end to reach 20 touchdowns. He also pulled within three of the single-season, tight-end record of 13 touchdown receptions held by Antonio Gates of San Diego and Vernon Davis of San Francisco.

Just 1:03 after Gronkowski’s second touchdown, Edelman got his second punt-return touchdown of his career as the Patriots jumped to a 24-3 lead with 9:24 left in the third quarter.

Arrington picked off another pass on the Chiefs’ next possession, leading to a 19-yard field goal by Gostkowski.

And just when it looked as if Palko, who had thrown just 13 passes before Monday night, might direct his team to a touchdown, he threw an interception to Phillip Adams in the end zone with 10:50 left in the game.

The Patriots finished the scoring on rookie Shane Vereen’s first NFL touchdown on a 4-yard run with 1:01 left.

In the last meeting between the teams, Brady went down with a season-ending knee injury in the 2008 opener and was replaced by Cassel. But he injured his right throwing hand in the Chiefs’ last game, a 17-10 loss, and had season-ending surgery on Nov. 14.

Palko completed 25 of 38 passes for 236 yards and three interceptions. Brady was 15 of 27 for 234 yards and no interceptions.

THE CHIEFS placed Cassel on injured reserve with a hand injury, ending his season.

He was placed on IR shortly before Monday night’s game.

The Chiefs filled Cassel’s roster spot with wide receiver Jeremy Horne, who has played in six games with the Chiefs in 2010 and 2011.

DEFENSIVE BACKS Patrick Chung and Devin McCourty were inactive for the Patriots.

Chung, a safety, missed his second straight game with a foot injury. McCourty, a cornerback, hurt his shoulder against the Jets on Nov. 13.

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