Carlos Santana homered and walked three times for the Indians, who took control with a five-run fifth and pulled away by scoring four in the seventh.
Kluber (5-3) became the first pitcher in the majors this season to have five straight outings with at least eight strikeouts. He gave up five hits, walked two and did not allow a runner past second base.
"Aside from throwing a lot of strikes, the biggest thing is working inside and outside," Kluber said. "I think the key is just working ahead. Getting ahead early and staying ahead in the count and not really letting them get comfortable up there."
Kluber is 3-0 with a 2.02 ERA and 48 strikeouts in five starts this month.
In this one, the right-hander dominated an offense that had produced 38 runs and 62 hits in its previous five games.
"Our game and our league, being able to be consistent is such a huge factor in becoming a really good major-league pitcher or player," Indians manager Terry Francona said. "That's what Klubes is doing. ... This is not like a shock or a big surprise. This has been coming."
Jimenez (2-6) matched zeroes with Kluber until the fifth inning, when the first-year Oriole was pulled without getting an out. Jimenez tied two undesirable season highs, giving up five runs and walking five, in four-plus innings.
"It looked like I was just missing a little bit of the strike zone," the right-hander said. "I'm not that far away, but I'm missing. I'm falling behind in the count, getting myself into trouble. Today was walking the leadoff guy."
Manager Buck Showalter suggested that Jimenez didn't get strike calls from home plate umpire Rob Drake on close pitches, and Jimenez agreed.
"I think I threw a lot of good pitches, but I don't know the umpire. He didn't like it," the pitcher said. "There's nothing I can do right now."
Jimenez spent 2 1/2 seasons with Cleveland before signing a $50 million, four-year contract with Baltimore in February.
"I didn't even think about who I was facing," he said. "When you get to the mound you are trying to get everybody out, it doesn't matter who it is. You have to do your job."
Jimenez struck out three and walked three in the first two innings, keeping the Indians hitless but using 52 pitches to do so.
"We got his pitch count up a little bit," Indians shortstop Justin Sellers said. "He got a little tired and he started leaving balls out over the plate."
Jimenez faced the minimum six batters over the next two innings, allowing an infield single to Michael Bourn before getting Michael Brantley to hit into a double play.
Then came the fifth inning, when seven batters reached before Baltimore got an out.
A walk, two singles and a throwing error by second baseman Jonathan Schoop produced the game's first run, and a single by Mike Aviles made it 2-0 and chased Jimenez. T.J. McFarland entered with the bases loaded and hit Brantley with a pitch to force in a run, and Lonnie Chisenhall followed with an RBI single. The final run of the inning scored on a double-play grounder.
In the seventh, Brantley singled and Chisenhall doubled before Ryan Raburn hit a two-run double. One out later, Santana hit reliever Brad Brach's first pitch over the right-field wall.
Before the game, the Orioles acquired C Nick Hundley (and cash considerations) from San Diego for LHP Troy Patton. Baltimore also recalled INF Steve Lombardozzi from Triple-A Norfolk. ... Orioles 3B Manny Machado missed a second straight game with a strained groin, but manager Buck Showalter said Machado was available if needed. ... Cleveland's Asdrubal Cabrera and Nick Swisher were both rested for a second consecutive game because of sore knees. ... Trevor Bauer (1-1, 2.25 ERA) goes for Cleveland in the series finale against Baltimore's Miguel Gonzalez (2-3, 4.53). ... Brantley threw out Steve Clevenger trying to stretch a single for his major league high sixth outfield assist. Brantley also extended his hitting streak to 10 games. ... Baltimore fell to 5-12 in day games, the worst record in the big leagues.
Copyright by STATS LLC and The Associated Press
BALTIMORE, MD - MAY 24: Ubaldo Jimenez #31 of the Baltimore Orioles pitches in the second inning during a...