The Diamondbacks couldn't solve Dodgers starter Josh Beckett through eight innings, but in the final frame Pollock touched him for a one-out double.
Miguel Montero was intentionally walked to set up a double-play, but Goldschmidt ruined the strategy by sending a 1-0 pitch through the hole into right field, easily scoring Pollock.
J.J. Putz (1-0) earned the decision with a scoreless top of the ninth for the D-backs, who took the rubber game of their three-game home series.
Arizona starter Trevor Cahill hurled 7 1/3 scoreless frames, scattering six hits with no walks while fanning four.
Beckett (0-2) absorbed the hard-luck loss, yielding six hits while striking out nine and issuing one walk.