Eric Young and Marco Scutaro got aboard with a pair of walks off Jamey Wright (1-1) in a 5-5 tie game. Scott Elbert came in to pitch, and Giambi, pinch-hitting for Dexter Fowler, sent a pitch into the Dodgers bullpen for the game-winner.
The big blow came only a half-inning after Los Angeles had forged a tie on Dee Gordon's two-out, two-run double off the glove of diving third baseman Chris Nelson.
Rafael Betancourt (1-0) earned the win despite yielding Gordon's hit.
Carlos Gonzalez smacked a pair of homers, driving in three runs, and Wilin Rosario also went deep for the Rockies, who took the rubber match of their three-game with the Dodgers.
Jerry Hairston Jr. drove in a pair of runs for the National League West-leading Dodgers, whose new ownership group was introduced Wednesday in Los Angeles.