Paxton (1-0), called up from Class AAA Tacoma earlier in the week, allowed two runs (one earned) on four hits in a six-inning performance. The rookie left-hander walked one and struck out three.
Morales went 3-for-4, socked a solo homer and added an RBI single, while Justin Smoak also went deep for the Mariners, who followed up Friday's series-opening 6-4 win with another victory.
Chris Archer (8-7) lasted only four innings for the Rays, yielding three runs (two earned) on four hits.
Evan Longoria cracked a two-run homer for Tampa Bay, which fell for the 11th time in 14 games and saw its lead in the American League wild card race dwindle to one game over Cleveland and Baltimore.