Giambi launched a three-run blast and added a two-run double while Reynolds also provided a three-run homer and Santana clouted solo shot to go along with an RBI double for the Indians, who banged out 22 hits.
Cleveland scored eight times in the first inning and followed that up with six more in the second, unleashing its biggest offensive output since 2009.
Corey Kluber (1-0) earned the decision with four innings of scoreless relief as Cleveland evened its three-game road series.
Astros starter Phil Humber (0-4) tumbled to his fourth straight loss beginning the season, surrendering eight runs on eight hits over just 1/3 of an inning.
Brandon Laird and Brandon Barnes homered and Ronny Cedeno supplied three RBI for Houston.