Garcia drove a 1-2 pitch from Cody Reed (0-1) the other way into the right-field stands. The native of Cuba leaped into the air and pumped his fists as he rounded first base, setting off a celebration in the Texas dugout as well.
"I was excited," Garcia said through a translator, adding it was special to hit the game-winner on Jackie Robinson Day.
“You could just see the joy when he's running around first base,” Rangers manager Chris Woodward said. “It's great to see.”
Garcia nearly hit his first homer Wednesday night, driving the ball off the top of the wall in right-center field and circling the bases amid confusion over whether it actually landed in the stands and bounced back onto the field.
The 28-year-old outfielder slid into home plate and was ruled safe. The call was overturned, leaving Garcia with a two-run triple that helped Texas finish a 5-1 victory.
“I told a friend, wait until tomorrow,” Garcia said, smiling. “I'll get one.”
Mike Brosseau homered for the Rays, who went 3 for 13 with runners in scoring position and stranded 12 overall.
“We're not making the the most of the opportunities we're getting,” Tampa Bay manager Kevin Cash said.
The defending AL champions have lost eight of 11 following a 2-0 start.
“The opportunities have been tough to come by lately,” Cash added, “but the ones we're getting, we've got to find ways to get more out of them.”
Culberson’s second homer of the series, a two-run shot off Hill in the fourth, gave the Rangers a short-lived 3-1 lead.
The Rays erased deficits with Austin Meadows' RBI single in the third, Brosseau's two-run homer in the fourth and without getting a hit in the seventh, when Brett Phillips walked and scored the run that made it 4-all with help from a pair of throwing errors.
The Rangers looked as though they might be on the verge of getting through the seventh unscathed when catcher Jose Trevino's errant pickoff throw to second base continued into center field, allowing Phillips to take off for third.
When center fielder Leody Taveras threw wildly past third as well, Phillips raced home to tie it.
Texas starter Jordan Lyles allowed three runs and five hits in 5 1/3 innings. Hill went 4 1/3 innings for Tampa Bay, yielding four runs and seven hits.
Rangers: With OF/DH David Dahl getting a night off, Trevino batted second — ahead of Joey Gallo and Garcia — even though he’s not a prototypical No. 2 hitter. Woodward explained: “Why wouldn’t I? ... I felt like I put a guy up there that’s obviously having the highest-quality at-bats and is one of our best hitters right now.”
Rays: SS Willy Adames and DH/INF Yoshi Tsutsugo were rested, but got called on to pinch hit in the 10th. Kennedy fanned both of them. ... CF Kevin Kiermaier (left quadriceps strain) will travel with the team to New York this weekend and could be activated during a six-game road trip against the Yankees and Kansas City Royals. “He ran well, threw well. ... We’ll see where we’re at (Friday),” Cash said after the defensive whiz worked out before the game.
Rangers: Return home to face Baltimore for three games before heading out on the road again. Mike Foltynewicz (0-2, 4.09 ERA) starts Friday against the Orioles, who counter with Jorge Lopez (0-2, 11.42) in the series opener.
Rays: Open a weekend series at Yankee Stadium. Cash entered Thursday night undecided on his pitching plans for Friday.
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