The Indians trailed 4-0 going into the bottom of the seventh with a three-run home run by Jose Lopez with two outs in the eighth tying the score 4-4.
Seattle took the lead in the 11th on Michael Saunders' double off the left-field wall but again the Mariners couldn't hold the lead.
Mariners' closer Brandon League (0-3) walked Lopez on four pitches to open the 11th. A wild pitch moved Lopez to second and, after an out and a walk to Kipnis, Asdrubal Cabrera singled in the tying run.
Kipnis went to third and League walked Aaron Cunningham on five pitches to bring up Santana with the bases loaded. He stroked a full-court pitch into center to end the game.
Joe Smith (4-1) pitched the 11th and got the win, despite giving up the Saunders' RBI double.
Saunders drove in the game's first run with a groundout in the third inning and the Mariners made it 2-0 in the fifth when John Jaso scored on a passed ball. Jaso doubled in a run and scored another in the sixth for a 4-0 lead.
Cabrera had a two-out single in the seventh to account for the first Indians' run and Lopez tied the score in the ninth with his second home run of the season.