NEW ENGLAND PATRIOTS tight end Rob Gronkowski (87) scrambles past Kansas City Chiefs defensive back Jalil Brown (30) during the first quarter of an NFL football game in Foxborough, Mass., on Monday. The Patriots rolled to a 34-3 victory.

Rob Gronkowski should be used to catching touchdown passes by now.

He already has 20 of them in less time than any tight end in NFL history, needing just 26 games. But there are moments when he has to remind himself how good he became so quickly.

“It’s still a dream come true being in the NFL,” Gronkowski said. “Some days I’ll wake up, I talk to Dane (Fletcher), my roommate, and we’re like, ‘Dude, we’re in the NFL.’ It’s crazy still. We still can’t kind of believe it.”

His production in just two NFL seasons is hard to believe. He added to it Monday night, catching two touchdown passes from Tom Brady as the New England Patriots overcame a sluggish start and beat the Kansas City Chiefs 34-3.

Gronkowski surpassed 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.

“Everyone’s doing their job and I just happen to be an open guy and Tom hits me in the end zone,” Gronkowski said.

That’s not all the 6-foot-6, 265-pound powerhouse does.

“He catches the ball great,” Brady said. “He’s tough. He runs well. He blocks. He really does everything you ask a tight end to do. He’s dangerous out there.”

Kansas City struggled offensively, not a big surprise with Tyler Palko making his first pro start after throwing just 13 passes in two seasons. He replaced Matt Cassel, who is out for the season with an injured right throwing hand. Palko completed 25 of 38 passes for 236 yards and three interceptions, two of which were tipped.

“All in all, I felt pretty confident,” Palko said. “Obviously, there’s a few things I’d like to have back.”

Kyle Arrington got two of the interceptions, increasing his NFL- leading total to seven.

“Turnovers and points off turnovers, that decides a game a lot in most cases,” he said.

The Patriots also got a big play on special teams as Julian Edelman returned a punt 72 yards for another score, putting New England ahead 24-3 with 9:24 left in the third quarter.

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

The Chiefs (4-6) lost their third straight and didn’t score after Ryan Succop’s 26-yard field goal gave them a 3-0 lead with 1:30 left in the first quarter.

“He did a fairly good job in the huddle,” wide receiver Steve Breaston said of Palko. “He did a great job executing the plays. We just have to help him out.”

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

Brady was under pressure early, but the protection improved. After throwing for just 19 yards in the first quarter, he led the Patriots on three consecutive scoring drives.

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

“When I get the ball, you just don’t want to go down,” he said. “You’ve got to try and do something with the ball. That’s why you get it.”

Arrington got his first interception on Kansas City’s next series and Stephen Gostkowski made it 10-3 at halftime with a 21-yard field goal.

“We were still fighting and we knew it was a close game going into halftime,” Chiefs safety Kendrick Lewis said. “They got a big play and a big score (Gronkowski’s second touchdown) in the second half and that started their rally.”

The Patriots got the ball to start the third quarter and went 85 yards on nine plays, scoring on Brady’s 19- yard pass to Gronkowski, who went head over heels, landing on his neck in the right corner of the end zone for a 17-3 lead.

“He’s a great football player,” Patriots guard Brian Waters said. “It doesn’t surprise me for him to be able to bounce up.”

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 held the Chiefs without a touchdown despite missing three key injured starters — linebacker Brandon Spikes, safety Patrick Chung and cornerback Devin McCourty.

“Every week we are going to go into practice and work hard,” Adams said, “regardless if (teams) are going to give us respect or not.”

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

Notes — Gronkowski’s 52- yard reception was the longest of his career. … The Chiefs tried an onside kick after Succop’s field goal but were called for touching the ball before it went 10 yards. … Wes Welker extended his streak to 88 games with at least one catch. His first reception didn’t come until six minutes remained in the game and he finished with two. … Starting 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 in the Patriots’ previous game, a 37- 16 win over the New York Jets. Also inactive for the Patriots were running back Kevin Faulk, linebackers Brandon Spikes, Jeff Tarpinian and Dane Fletcher, and quarterback Ryan Mallett.