Tampa Bay (21-22) finished its road trip 5-3. Miami (23-22) concluded its homestand 2-3.
Odorizzi (2-2) earned the win. Tom Koehler (2-5) took the loss after allowing three runs in five innings.
The Rays cooled off Marlins left fielder Ichiro Suzuki, who went 0-for-4 after a 10-for-13 performance over his past three games.
But Miami’s Giancarlo Stanton, who endured a brutal 5-for-52 slump with 28 strikeouts, extended his modest hit streak to three games and homered for the first time since May 15. Stanton drilled a 94 mph low fastball from reliever Enny Romero for a solo shot.
Logan Morrison, a former Marlins player who went 3-for-3, scored the game’s first run. He singled, stole second, went to third on a fly out to center and scored on pitcher Odorizzi’s lined single to right on a pitch up in the zone.
Tampa Bay stretched its lead to 3-0 in the fourth. Morrison drew a one-out walk and advanced to third on Corey Dickerson’s double. Both runners scored when Hank Conger, who entered the game batting just .157, lined a two-run single just past the glove of Marlins first baseman Justin Bour, who dove for the ball.
Miami had a chance to get back in the game in the bottom of the fourth, loading the bases with two outs. But Adeiny Hechavarria’s drive to right field was caught on the warning track by Steven Souza.
With Odorizzi out of the game, the first batter faced by Romero was Stanton, who slugged his 12th homer of the season to lead off the bottom of the sixth. Marcell Ozuna, who has reached base in a career-high 31 games, doubled and scored on Derek Dietrich’s single, cutting Tampa Bay’s lead to 3-2.
Tyler Sturdevant, a 30-year-old right-hander who made his major-league debut after eight seasons in the minors, got Tampa Bay out of that sixth-inning jam. Sturdevant retired both of the batters he faced, striking out Hechavarria and getting pinch hitter Chris Johnson to bounce out.
Tampa Bay took a 4-2 lead in the seventh. Brad Miller walked, stole second, advanced to third on a throwing error by catcher J.T. Realmuto and scored on a single by Steve Pearce.
Miami cut its deficit to 4-3 in the eighth. Ozuna doubled and scored on a two-out single by Hechavarria.
NOTES: This four-game series continues the next two days in Tampa Bay. … The 10 hits over the past three days by Marlins LF Ichiro Suzuki, 42, were the most by a player his age or older since Cap Anson did it in 1894. … Suzuki’s 10 hits in three games also tied the franchise record held by Hanley Ramirez, Luis Castillo and Preston Wilson. … The Rays, who lead the majors in home runs, hit one more long ball than even the famed Big Red Machine of Cincinnati had through 42 games in 1970. … Rookie SS Taylor Motter reached two homers and five RBIs in just six major-league games, just the second Rays player ever to accomplish that feat, tying Delmon Young. … The Rays had the second-worst offense in baseball in April (3.30 runs) but have had the second-best offense in May (5.47).