The game was called after nine innings.
Kluber gave up one run and three hits, striking out one without a walk. He went 18-9 with a 2.44 ERA last season.
"I wasn't very sharp and I didn't do a very good job of getting ahead of guys," Kluber said. "But I felt good physically, so that's the important thing."
Kluber, who turns 29 on April 10, allowed an RBI single to Yasmani Grandal in the first inning.
Grandal homered and had three hits for the Dodgers. Acquired from San Diego in the deal for Matt Kemp, Grandal homered off Zach McAllister in the fourth.
Grandal nearly homered again in the sixth, driving another pitch from McAllister off the top of the wall in left-center, 380 feet away, for an RBI single. Grandal was thrown out trying to stretch it into a double.
Dodgers slugger Adrian Gonzalez doubled in a run in the sixth.
The Indians tied it with four runs in the bottom of the ninth off Matt Shelton. Ryan Rohlinger hit a three-run homer and Brett Hayes followed with a home run.
"They really did outclass us today," Indians manager Terry Francona said. "That happens. I'm glad we did it. But when you are facing (Nos.) 88 and 89, that happens."
Dodgers: LF Carl Crawford fouled a pitch off his right shin and came out of the game as a precaution. He is day to day. Los Angeles manager Don Mattingly said Crawford has a scheduled day off coming up. His status will be evaluated throughout the week. ... LHP Hyun-Jin Ryu threw two innings (36 pitches) of batting practice after complaining of mild back stiffness. He's tentatively scheduled to make his Cactus League debut Thursday night in Peoria vs. San Diego. ... Right-handed reliever Joel Peralta (shoulder stiffness) threw a bullpen session. His next step is live batting practice. Peralta, acquired in a four-player deal with Tampa Bay after posting a 4.41 ERA in 69 appearances last season, is on the mend from shoulder stiffness.
Indians: 2B Jason Kipnis, recovering from an injury to his left ring finger, went 0 for 2 in his spring debut. Kipnis was an All-Star in 2013, when he hit .284 with 17 homers and 84 RBIs. His numbers slid last year to .240 with six home runs and 41 RBIs.
Right-hander Chad Gaudin followed Bolsinger and made his first appearance since the 2013 season. Gaudin struck out three in two scoreless innings, allowing one hit. He went 5-2 with a 3.06 ERA (30 games, 12 starts) for San Francisco in 2013.
Dodgers: Bolsinger made his first start of the spring. He worked two innings, allowing two hits and a run. The Dodgers purchased Bolsinger from Arizona in November. He went 33-21 with a 3.49 ERA over five minor league seasons.
Indians: Kluber threw 39 pitches and then another 12 in the bullpen afterward. "He looked really good," Francona said. "He just didn't command the way he will." Kluber is prepared for the rest of the league to try to adjust to him after his Cy Young season. "I think that's part of the game," he said. "There are always adjustments going on, whether it be the batter or the pitcher."
Dodgers: RHP Brandon McCarthy makes his spring debut Sunday when the Dodgers host Milwaukee in Glendale. McCarthy had a solid stint with the New York Yankees in 2014, starting 14 games and going 7-5 with a 2.89 ERA. Before that, he was 3-10 with a 5.01 ERA in 18 starts with Arizona. He signed a $48 million, four-year contract with the Dodgers in the offseason.
Indians: LHP T.J. House will make his first start of the spring when the Indians travel to Surprise to face the Texas Rangers on Sunday. House went 5-3 with a 3.35 ERA last season.