Steven Souza Jr.'s simple approach at the plate is working.
"Just letting my ability play," Souza said. "I can really overthink things, and put a lot of pressure on myself. Throughout the years, I think that's what I've done."
Souza doubled in the first, hit a two-run triple in the second and added a solo homer in the eighth. He has reached base multiple times in 12 games this season.
"I think we're seeing him put it together," Rays manager Kevin Cash said.
Ramirez (2-0) allowed one run and two hits in five innings with five strikeouts and no walks. In the rotation because Jake Odorizzi strained his left hamstring, Ramirez had not started since April 16 last year.
Chase Whitley gave up a hit and two walks in three innings, and Tommy Hunter allowed two hits in the ninth.
Tampa Bay rookie Daniel Robertson hit his first career homer, an eighth-inning solo shot off Warwick Saupold.
The Tigers were outscored 21-9 in series and while making just two errors allowed several catchable balls to fall for hits.
"I'll be honest with you, this is the worst defensive series I've seen the Detroit Tigers play since I've been here," manager Brad Ausmus said.
Daniel Norris (1-1) gave up five runs and eight hits over 4 2/3 innings.
Ian Kinsler hit his 41st leadoff homer, but Tampa Bay tied the score in the bottom half after Souza doubled on a fly ball that right fielder Tyler Collins appeared to lose. He scored when Dixon Machado, filling in for injured shortstop Jose Iglesias, made an errant throw after fielding Rickie Weeks' grounder.
Souza tripled on an opposite-field flare that bounced past Collins near the right-field line, then scored on Kevin Kiermaier's single for a 4-1 lead.
Kiermaier homered off Saupold in the seventh.
Saupold was optioned to Triple-A Toledo after the game, and left-hander Blaine Hardy will be recalled from the International League club.
The game started with just three umpires because crew chief Larry Vanover left due to a personal matter. Joe West was brought in to fill out the crew and arrived to take the field in the bottom of the first.
Tigers: OF Justin Upton (bruised right forearm) was out of the lineup for the second straight game but is swinging a bat. ... Iglesias was hit on the jaw by the knee of a sliding Brad Miller in the ninth inning Wednesday night after stumbling over second base and then making a bad throw to first on a potential game-ending double play as the tying and winning runs scored. Ausmus said Iglesias still had a headache and his status "will be determined in the near future."
Rays: OF Colby Rasmus (hip surgery) is scheduled to resume his minor league rehab assignment Saturday with Double-A Montgomery. He has not played the past two weeks due to a sore knee.
Norris entered without a loss in his first 16 career road starts, which tied Todd Wellemeyer and Larry Jansen for the second longest stretch since 1913. Only Dave LaPoint has more with 20.
Tigers: RHP Justin Verlander (1-1) looks to rebound Friday night against Minnesota after allowing a career-high-tying nine runs Saturday at Cleveland. He has won 12 of his last 13 decisions against the Twins, dating to July 9, 2010.
Rays: RHP Alex Cobb (1-1) goes against Houston RHP Mike Fiers (0-1) Friday night.