Jimenez (9-7) allowed only one hit and overcame five walks in breaking a personal two-start losing streak. The right-hander struck out eight.
Relievers Rich Hill, Bryan Shaw, Joe Smith and Matt Albers combined to blank the A's the rest of the way as the Tribe bounced back from a 3-2 loss in Friday's three-game series opener.
Dan Straily (6-7) was touched for three runs on six hits over 5 2/3 innings for the Athletics, who fell 1 1/2 games behind American League West-leading Texas.
Josh Donaldson produced Oakland's only RBI.
Swim Week Miami Beach 2014 [PHOTOS]