The Astros, who had dropped three in a row and are already assured a losing record this season, came up with 15 hits and built a 10-2 lead through five innings.
Houston's attack was highlighted by a five-run fourth inning in which triples by Brandon Barnes and Jason Castro accounted for three runs.
Grossman had a sacrifice fly during the big fourth frame, brought home another run with a single in the fifth and hit a two-run homer in the seventh.
Jordan Lyles (6-6) gave up four runs on 10 hits in 7 1/3 innings, but was still the easy winner. Todd Redmond (1-2) was touched for seven runs and eight hits in just 3 1/3 innings.