Trailing 3-1 entering their final at-bat, the Diamondbacks struck for four runs against Brandon League (2-3) and Peter Moylan to pull out the victory.
Didi Gregorius then drew a walk to load the bases, and Bloomquist followed by sending a grounder deep into the hole that Dodgers shortstop Nick Punto dove to stop. But the ball popped out of his glove, allowing Parra and Kubel to score.
Moylan entered and allowed a run-scoring single to Paul Goldschmidt -- a run Arizona would need when Juan Uribe homered for Los Angeles in the bottom of the ninth.
Tony Sipp (3-1) earned the win and Heath Bell struggled in the ninth but recorded his 12th save as the National League West-leading D-backs improved to 16-3 in their last 19 meetings with Los Angeles.