Garcia hit his second career grand slam on Tuesday in a 9-5 victory that opened the series. He delivered the big blow a day later with a bases-clearing double in the eighth inning to give the Indians a 6-2 cushion.
Terry Mulholland relieved Cleveland starter Danys Baez (9-9) after the fifth inning and tossed three scoreless innings before John Flaherty led off the ninth with a double and Jason Conti tripled him home.
Wohlers came on and allowed an RBI groundout by Andy Sheets. Chris Gomez also grounded out, but All-Star Randy Winn reached on an error by second baseman Ricky Gutierrez to bring up the tying run in rookie Carl Crawford. Wohlers struck out the Devil Rays' top prospect on three pitches for his sixth save.
Ellis Burks went three for four and got his 2,000th hit with a single in the first inning. Burks gave Cleveland the lead for good in the fifth, hitting an RBI single for a 3-2 advantage.
Tampa Bay starter Paul Wilson (5-8) had his three-game winning streak stopped after allowing four runs and nine hits in 7 1/3 innings.