Kershaw, the 2014 National League MVP and Cy Young Award winner, threw 45 pitches while facing 11 batters and gave up one hit and an unearned run. He'll next face the San Diego Padres on April 6.
"I was still a little bit all over the place," Kershaw said. "I walked two guys in three innings. We don't want to do that. And then had a couple of hard hit balls right at guys. Definitely, room for improvement, but physically I feel good and ready to go. That's all you can ask for at this point."
Kershaw had a 1.61 ERA this spring. He gave up just 15 hits and struck out 22 in 22 1/3 innings this spring.
Brett Eibner homered twice for the Royals, including a two-run shot in the ninth to tie it. Eibner tops the club with five home runs, but will begin the season in the minors.
Ventura, who threw seven no-hit innings against Seattle in his previous start, yielded two runs, one earned, and four hits in four innings.
The Dodgers played seven ties, a club spring training record.
Dodgers: Kershaw will be making his fourth consecutive opening-day start. "Clayton looked like a guy who was gearing up for opening day," catcher A.J. Ellis said. "It's always a challenge with him, pitching when he knows he has an expiration date on his game. There's really no reward at the end for him as far as wins and losses. You saw last year the way his spring regressed and then how he turned the corner on opening day. It's something about the adrenaline and the competition rush that takes him to another level. He's gotten to the point in his career, especially who he is and the stature that he has that spring training is probably not his favorite time of the year."
Royals: Ventura, who will start the Royals' opener Monday against the Chicago White Sox, threw 41 strikes in 61 pitches.
GREINKE'S MINOR WORK
RHP Zack Greinke threw 85 pitches and seven innings in a minor league intrasquad game. He allowed two runs, both on homers, and five hits, while striking out nine.
Dodgers: OF Andre Ethier was struck in the right elbow by White Sox LHP Carlos Rodon Tuesday. X-rays were negative.
Royals: RHP Luke Hochevar, who had reconstructive elbow surgery during last spring, will begin the season on the disabled list. He will likely be ready by early May. He pitched a flawless inning Wednesday.
HIGHLAND PARK DAY
Kershaw and Royals RHP Chris Young, who gave up a home run to minor leaguer Travis Witherspoon in the seventh, are graduates of Dallas Highland Park High.
Dodgers: A host of relievers will pitch against the Angels Thursday in Anaheim.
Royals: The Royals, who are off Thursday, will start RHP Edinson Volquez Friday against the Astros at Houston.