Kennedy pitched two-hit ball and struck out 10 over eight innings as Kansas City sent the Angels to their fifth loss in a row.
''My fastball command was down,'' Kennedy said. ''It was up when I needed it to. All my misses were down. When I needed to go up, it was there.''
Kennedy didn't allow a hit until C.J. Cron's double with two outs in the fifth. Cliff Pennington singled with two outs in the eighth for the Angels' other hit.
''That's a tough lineup to navigate through,'' Kennedy said. ''They have two of the best three-and-four hitters you'll face in a year with (Mike) Trout and (Albert) Pujols.''
Kennedy struck out 10, his 13th double-figure strikeout game, and walked two. He entered the game with an 0-4 record and 6.55 ERA in five career appearances against the Angels.
''He threw the ball well, he kept the ball down, and obviously he kept us off-balance,'' Pujols said. ''That's pretty much it. Both sides threw the ball well.''
Salvador Perez led off the ninth with a single against Blake Parker (0-1), and pinch runner Raul Mondesi stole second and went to third on a wild pitch.
After pinch hitter Mike Moustakas walked, Cam Bedrosian relieved and Paulo Orlando fouled out. Escobar followed with his game-winner.
With the Angels using a five-man infield and two outfielders playing shallow, Escobar lofted a single to right-center over Trout's head.
''I was trying to elevate the ball,'' Escobar said. ''I'm trying to get a fly ball in that situation. I'm looking for one pitch and I hit the ball good.''
Herrera (1-0) threw a flawless ninth.
Angels left-hander Tyler Skaggs, who had an 8.71 ERA in his first two starts, threw seven shutout innings, giving up four hits and striking out nine. He allowed three hits and walked one in the first two innings.
''I don't know if impressive is the right word, but he definitely made some adjustments,'' Angels manager Mike Scioscia said. ''I think that if he can carry that rhythm over, you're going to see a guy that can do what he did today on a consistent basis. Getting his pitches in the zone; his process was great. He changed speeds. So, that was a terrific outing.''
PERFECT ON CHALLENGES
The Royals, under the guidance of replay specialist Bill Duplissea, are 5 for 5 in challenges this year. Duplissea won 27 of 39 challenges last year, a 69.2 percent success rate that topped the majors.
Angels: RHP Huston Street (right lat strain) is playing catch, but is likely three weeks to a month away from returning. Street was injured in his first spring training outing.
Royals: OF Jorge Soler (left oblique strain) had a setback in his rehab, feeling tightness after batting practice Saturday. He has been backed off a couple of days from activity.
Angels: RHP Jesse Chavez will start Monday at Houston as they continue this trip. He is 3-1 with a 2.90 ERA in 23 career games against the Astros.
Royals: Off Monday before hosting San Francisco to open a two-game series Tuesday. Royals RHP Jason Hammel will start the first game.