Howie Kendrick added two RBI and Collin Cowgill drove in a run for the Angels, who have taken the first two games of this series.
Los Angeles was just 5-for-19 with runners in scoring position and left 14 runners on base.
Corey Kluber (2-3) allowed four runs -- three earned -- on eight hits and four walks over 4 2/3 innings.
The Halos jumped out to a 1-0 lead in the second inning. With two on and no outs, Iannetta singled to left to score David Freese.
The Angels added another run in the fourth and two in the fifth to take a 4-0 lead. In the fourth, Iannetta reached on a fielding error before moving to third on J.B. Shuck's base hit. Cowgill followed with a base hit to right to score Iannetta.
Cowgill drew a two-out walk in the fifth before Kendrick ripped a base hit to center to score Freese and J.B. Shuck.
Santana got the Tribe on the board in the sixth with a two-run homer to right- center field. Mike Aviles singled before Santana cracked a change-up over the fence.
In the home half, Aybar ripped a chopper up the middle that deflected off Scott Atchison's glove to plate Albert Pujols and make it 5-2.
The Indians added two more runs in the seventh. Nick Maronde replaced Yoslan Herrera with the bases loaded and no outs and walked Santana on four pitches. Brantley followed with a sacrifice fly to left to score Lonnie Chisenhall and make it 5-4.
The Halos added an insurance run in the eighth. Aybar singled, moved to second on a balk, then scored on Iannetta's single to left field.