Seager's clout in the third put Seattle ahead 3-0 and Montero's blast in the next frame broke the contest open, sending the M's to a victory in the opener of a three-game series.
Morales went deep in the fifth and Montero added a sacrifice fly to finish with three RBI in the victory.
Felix Hernandez (2-2) struck out nine over six scoreless innings to notch the decision. The Mariners' ace issued only one walk en route to the victory.
Astros starter Brad Peacock (1-2) was tagged for seven runs on nine hits in a 4 1/3-inning effort.
Rick Ankiel supplied a solo homer for hapless Houston, which fell for an eighth time in nine games.