KANSAS CITY, Mo. — CC Sabathia’s eyes light up whenever he sees the outfield fountains at Kauffman Stadium.

His performance usually picks up, too.

The Yankees’ big left-hander carried a shutout into the seventh inning Tuesday night, getting a three-run homer from Gary Sanchez and a two-run shot from Chris Carter in support, and New York went on to rout the Kansas City Royals 7-1 in the opener of their three-game series.

Pitching on six days’ rest, Sabathia (3-2) struck out five and walked two over 6 2/3 innings to win for the first time since April 15. And the fact he got back on track in Kansas City should come as no surprise: He is 13-5 in 21 career starts there, matching the record for most wins by a visitor.

“I love pitching here,” Sabathia said, smiling. “It’s my favorite park.”

Sabathia was never in trouble until the seventh, when Alex Gordon’s infield single loaded the bases with two outs. Tyler Clippard came in and fanned Whit Merrifield to escape the jam, then handled the eighth before Jonathan Holder allowed a run in the ninth.

That preserved the solid effort by Sabathia, who had allowed 22 runs in his last four starts.

“He was pretty frustrated with the way things were going,” Yankees manager Joe Girardi said, “not pitching the way he did earlier this season. So I think this was big.”

Sanchez drilled an 0-1 pitch from Jason Hammel (1-5) to center field with nobody out in the third, and Carter pounded a 1-1 pitch to almost the same place with two down in the fourth.

“I’ve got to do a better job of keeping the ball in the park,” Hammel said. “Both the guys that hit it out are strong boys. They’re mistake killers.”

Jacoby Ellsbury and Matt Holliday also drove in runs against the Royals’ bullpen, part of a 13-hit outburst that sent the Yankees to their ninth win in the last 11 meetings with Kansas City.

It was another dismal night for Hammel, who allowed seven runs over seven innings in his last start against Tampa Bay. The right-hander yielded five runs on nine hits and a walk in six innings this time, and has served up six home runs in his last four outings.

“It was two balls that left the yard that hurt me,” he said. “I’m trying to stay positive and just continue to work. I’ve got to find a way to do a better job of establishing a better tone early.”

Meanwhile, Sabathia was getting plenty of help from his defense.

Alcides Escobar twice lined out to third baseman Chase Headley, including a hot shot leading off the game. Carter made a couple of nifty plays at first base, and left fielder Brett Gardner threw out Jorge Soler in the fifth inning as he tried to stretch a single.

The Yankees’ dominant pitching and defense came after the Royals had won three one-run games in a sweep of Baltimore, capped by a season-best 14 hits in the finale on Sunday.

“We had guys hit the ball on the nose,” Royals manager Ned Yost said, “and not much to show for it.”

STATS AND STREAKS

Sanchez has hit all three of his homers on the road this season. … Carter has 13 career hits against Kansas City. Six of them are home runs. … The Royals were held to one run or fewer for the 13th time, most in the majors. … Gordon had his first multi-hit game since April 9.

SILENCE FOR STEVE

There was a moment of silence before the game for Steve Palermo, the umpire whose career ended when he was shot trying to break up a robbery in 1991. Palermo, who lived in the Kansas City area, died last weekend at age 67. He had been ill with cancer.

TRAINER’S ROOM

Royals RHP Ian Kennedy will throw a bullpen Wednesday and hopes to make his next start Saturday. Kennedy has been dealing with a strained right hamstring.

UP NEXT

Yankees RHP Michael Pineda tries to keep rolling when he gets the ball Wednesday night on five days’ rest. Pineda is 3-1 with a 2.63 ERA over his last six outings.

Royals LHP Jason Vargas makes his ninth career start against the Yankees, still searching for his first win. He is 5-1 with a 1.01 ERA this season, but 0-5 with a 6.53 ERA vs. New York.