The Marlins' bullpen squandered an 8-1 lead by coughing up seven runs in the seventh inning, three stemming from bases-loaded walks. Miami's offense, which scored just three runs in a season-opening sweep at the hands of the Braves, bailed them out.
David DeJesus hit a pinch-hit, three-run triple to highlight Tampa Bay's seventh inning, but the Rays nevertheless fell to 1-3 on the young season. Kevin Kiermaier homered and drove in a pair of runs in defeat.
David Phelps was quickly given the hook after walking Logan Forsythe with the bases loaded, and Sam Dyson gifted the Rays two more runs with run-producing walks to Brandon Guyer and Kiermaier.
A.J. Ramos was brought in to clean up the mess, but he too fell behind in the count to DeJesus, who barreled up a 3-1 offering and nearly cleared the right- field wall. He settled for a three-run triple then scored the tying run when Asdrubal Cabrera's dribbler got under the glove of a diving Gordon.
Gordon bunted into a force out in the eighth and stole second to get into scoring position for Stanton, whose sharp line drive to center off Bobby Wilson easily scored the go-ahead run.
Steve Cishek could not close out the win in the ninth, however. With runners on the corners and one out, the Marlins were unable to turn a double-play off the bat of Cabrera, and Brandon Guyer scored the tying run.
Gordon doubled off Brad Boxberger (0-1) with one away in the 10th and scored without a play at the plate when Yelich sent a gapper to left.
Bryan Morris (1-0) earned the win by tossing a scoreless 10th.
The Rays were forced to start reliever Steven Geltz since Alex Cobb, Drew Smyly, Matt Moore and Alex Colome are all on the disabled list. Geltz, who had never made a start in the minors or majors, gave up a run over two innings.
Morse singled in Yelich in the first inning, and his double play with the bases loaded in the third pushed across Gordon.
Kiermaier led off the fourth with a homer down the right-field line, and the Marlins countered with a six-spot off Erasmo Ramirez in their half to seemingly take control.
Adeiny Hechavarria's first hit of the season was an RBI double, Yelich and Stanton both drove in a pair, and Morse capped the big frame with run-scoring single.
Haren, who arrived in Miami in an offseason trade with the Dodgers, limited the Rays to one runs on four hits over the first six frames ... The Marlins avoided matching a club-worst 0-4 start ... The Rays are 3-15 all-time in road openers ... This was the first game of six this season in the annual Citrus Series ... The Marlins swept all four meetings from the Rays last season.