Jimenez (9-7) didn’t allow a hit until Josh Donaldson lined a run-scoring single to shallow center with two outs in the sixth, ending the pitcher’s night after 105 pitches. He struck out eight and walked five.
Asdrubal Cabrera drove in two runs and Michael Brantley hit a pair of doubles for Cleveland.
A day after the Indians matched a season high with 13 stranded base runners, they took advantage of timely opportunities.
Swisher drove the first pitch from Dan Straily over the right-field fence for his 13th home run, staking Jimenez to an early lead in the first. Cabrera later added a run-scoring single before hitting an RBI double in the sixth.
Pitching on six days’ rest, Jimenez bounced back after taking a 7-2 loss to the Angels on Aug. 10 for his second straight defeat.
The A’s drew two walks from the right-hander in each of the third and fourth innings but failed to capitalize.
Jimenez plunked Josh Reddick in the right shoulder with one out in the sixth and Rich
Hill began warming up in the bullpen. Jimenez walked Yoenis Cespedes on his 101st pitch and received a mound visit from pitching coach Mickey Callaway.
Brandon Moss then struck out swinging before Donaldson singled.
The A’s didn’t do much more.
Coco Crisp flied out as a pinch-hitter with runners on the corners to end the eighth.
Bourn’s seventh-inning drive ended an 0-for-11 stretch for just his second hit in 21 at-bats during the team’s road trip.
Swisher added an RBI single and Jason Kipnis a two-run single in the ninth as the Indians won for the fifth time in the first six meetings with the A’s after sweeping a four-game set at home in May.
Straily (6-7) extended his losing streak to five games. He is winless in six outings since being recalled from Triple-A Sacramento on July 20, though he had received no run support in three of those outings since the All-Star break.
He allowed three runs and six hits, struck out seven and matched his season high with four walks over 5⅔ innings.
Straily allowed Swisher’s one-out homer then struck out Kipnis before allowing back-to-back walks to Carlos Santana and Brantley. Pitching coach Curt Young made a mound visit when he went 2-0 to Cabrera, who then hit an RBI single to snap an 0-for-20 streak.
After Drew Stubbs doubled to start the Cleveland fifth, Gold Glove right fielder Reddick started a sensational double play when he caught Bourn’s liner and made the perfect throw to third to get Stubbs.
The sold-out Coliseum crowd of 35,067 booed former A’s fan favorites Swisher and Jason Giambi whenever they came to the plate.
Cespedes went 1-for-3 with a walk on a day fans arrived more than four hours early to get his bobblehead.
The Indians scored in the opening inning for the first time since Aug. 3 at Miami and put up multiple runs in the first for the first time since July 24 at Seattle.
* Crisp took batting practice but didn’t start for a fourth straight game because of a sore left wrist, yet he stayed in the game at CF for the ninth. Crisp received a cortisone injection Tuesday.
* The Indians are 18-7 against the AL West with eight games to go.
* A’s RHP Bartolo Colon is headed to the 15-day disabled list today with a strained left groin after he was hurt throwing on flat ground Friday. Oakland will recall lefty Tommy Milone from Triple-A to start the series finale today.
* Indians RHP Josh Tomlin, who hasn’t pitched all year as he works back from Tommy John surgery, got through his rehab outing with Double-A Akron with positive results. Francona said he likely won’t rejoin Cleveland until rosters expand in September.