Jimenez (10-9) walked two and struck out four in the 90-pitch performance.
Asdrubal Cabrera delivered a pair of sacrifice flies for a 2-0 Indians lead and Gomes doubled the advantage with a game-clinching two-run double in the sixth.
The Indians ended up needing the extra runs when Baltimore's Nate McLouth bashed a three-run homer in the ninth, but closer Chris Perez got the next three outs to end the game as the Tribe rebounded from a 7-2 loss in Monday's three-game series opener.
They came into the contest trailing American League wild card leader Tampa Bay by 3 1/2 games -- 1 1/2 games further back than the Orioles and one behind the New York Yankees.
O's starter Chris Tillman (15-5) was touched for four runs on five hits in a 5 1/3-inning effort.