Trailing 2-1 entering the frame, the Cards erupted for three runs to chase Giants starter Ryan Vogelsong and grab the lead.
Holliday's single with two on and two out drove in the tying run, and after Allen Craig got a base hit, Beltran delivered a two-run single for the decisive blow.
Beltran finished with three RBI and Pete Kozma went 3-for-4 with a run-scoring single for St. Louis, which evened its three-game series.
Matt Carpenter added an RBI in the win.
Shelby Miller (1-0) earned the victory in his second major-league start, allowing two runs on four hits with four strikeouts over 5 1/3 innings
Miller overcame four walks en route to the decision.
Vogelsong (0-1) was roughed up for five runs on nine hits over 5 1/3 frames.