The Diamondbacks forged a 3-3 in the seventh on a pinch-hit Eric Chavez sacrifice fly and the game remained knotted until the 10th, when the Arizona third baseman again came through with a one-out single off Luis Perez (0-1).
Eaton came in to run for him and went to third on A.J. Pollock's single against Jeremy Jeffress.
That brought up Bloomquist (3-for-5), who delivered the D-Backs' third straight single -- a line drive that got past diving second baseman Ryan Goins for the game-winning run.
Will Harris (3-0) earned the decision for the D-backs, who avoided a three-game sweep.
Rajai Davis smacked a two-run homer for Toronto.