The Indians seemed on their way to a victory with a 4-2 lead in the top of the ninth inning, but Raul Ibanez and Justin Smoak hit back-to-back solo homers with two out off Tribe closer Chris Perez (2-0), to tie the score.
Kipnes led off the bottom of the ninth with a single against Oliver Perez (1-1) and went to third on a double off the left-field wall by Asdrubal Cabrera (3-for-5). Nick Swisher was intentionally walked to load the bases and Yoervis Medina came in to pitch.
Reynolds then sent a grounder to shortstop Brendan Ryan, whose throw home pulled catcher Jesus Montero off home plate, allowing Kipnes to score the game-winning run.
Reynolds socked a solo homer and finished with three RBI for Cleveland, which improved to 13-3 in May.
Ryan went 2-for-3 with a solo homer for the Mariners.