James Paxton (1-0) earned his first career MLB victory after allowing two runs -- one earned -- on four hits and a walk over six frames for Seattle, which has won three of its last four games.
Chris Archer (8-7) surrendered three runs -- two earned -- on four hits and a walk over four frames for the Rays, who have dropped three in a row and eight of its last 10 tilts.
Tampa Bay, though, still holds a slim one-game margin over the Cleveland Indians and Baltimore Orioles for the AL's second wild-card spot.
Evan Longoria's one-out, two-run homer to left in the sixth pulled the Rays within 4-2 before Seattle answered with a pair of runs in the home half on a pair of RBI doubles by Michael Saunders and Nick Franklin to make it 6-2.
Chance Ruffin and Lucas Luetge combined to fire a scoreless eighth and Danny Farquhar blanked the Rays in the ninth to seal the outcome.
Earlier, Seattle jumped out to a 4-0 lead after it plated a run in each of the first three frames and tacked on another in the fifth.
Morales' two-out RBI single got Seattle on the board in the opening frame. Solo shots by Justin Smoak and Morales in the second and third innings, respectively, preceded Abraham Almonte's RBI bunt single in the fifth to vault the M's to their four-run cushion.
The Mariners were 2-for-8 with runners in scoring position, while the Rays finished 0-for-4 with RISP ... Longoria's homer was his 29th of the season, while Morales' shot was his 19th.
09/08 01:04:30 ET