The two-out double went just past the outstretched glove of first baseman Carlos Pena to bring home Leonys Martin, who pinch-ran for Geovany Soto following his double. Reliever Kyle Farnsworth would eventually load the bases and hit Josh Hamilton, giving Texas an insurance run.
"As soon as Geo got that double, it was, 'Thank you, we got them,'" Profar said. "It's a good first two games."
The Rangers were in position to win earlier, but an error by second baseman Ian Kinsler on a grounder from Pena allowed the Rays to score in the bottom of the eighth, tying the game and putting Tampa Bay in position to steal another game from Texas.
"They took one from us last night and almost snatched one away from us today after leading the whole game, but the guys didn't quit and kept fighting," Rangers manager Ron Washington said.
With the win, Texas maintained its 4 1/2-game lead over Oakland, who defeated Seattle, in the American League West. Washington said a close, low-scoring game like Saturday's matchup doesn't prepare them any better down the stretch, though.
"You don't know what the game is gonna offer from night to night," Washington said. "I don't think you think about what's preparing you for this and what's preparing you for that. You gotta stay focused on what you gotta do to win a ballgame today."
The Rangers spoiled a great game by Yu Darvish, who allowed one earned and one unearned run on two hits, two walks with eight strikeouts over eight innings.
"Today I felt good with my four-seam fastball," Darvish said through an interpreter. "I felt like I had good command with it pitching early but in the middle of the game, my command started getting iffy a little bit. But my cutter, my command of that was good all the way through."
The offense continued to struggle against Rays pitching most of the night. After being held to one run in 11 innings on Friday, the Rangers scored just two on four hits through the first nine innings. The lineup made up for it in the 10th though, scoring twice on three hits, a walk and a hit batter.
Chris Archer made the start for the Rays in place of David Price, allowing two runs and four hits with two walks, a hit batter and 11 strikeouts over seven innings.
"Every time I go out there, I expect greatness," Archer said. "I'm giving 100 percent intent with every pitch."
Both pitchers dominated the first time through the order in the first three innings. Each allowed just one hit and combined for nine strikeouts.
Texas finally got on the scoreboard in the fourth inning when Hamilton blasted an 0-1 pitch to straightaway center field for a two-run homer, his fifth in the last 10 games.
"I didn't execute the pitch," Archer said. "I was trying to throw a good slider down and in, and it wasn't a good slider. It was up and over the plate."
Hamilton, who leads the Majors in homers, became just the fifth player in club history to reach 40 home runs in a single season, joining Juan Gonzalez, Rafael Palmeiro, Alex Rodriguez and Mark Teixeira.
"That's what good hitters do," Washington said. "Hamilton is definitely one of the best in the American League and all of baseball. The kid threw him a slider, he stayed inside of it and drove it to center field and gave us a lead right there."
Archer wasn't as kind the next time he faced Hamilton, hitting him with a pitch near the ear hole of Hamilton's helmet, prompting both benches to be warned and Washington wanting an explanation.
"[Home-plate umpire Mike Estabrook] just wanted to keep the game in check, he didn't want the game to get out of control," Washington said.
Darvish, meanwhile, continued to breeze until a bumpy sixth inning that saw him give up a leadoff single to Jeff Keppinger, the Rays' first baserunner since the first inning. Ryan Roberts then drew a walk and both runners advanced on a wild pitch. A Sam Fuld grounder allowed Keppinger to score from third, making it 2-1.
Tampa Bay scored again in the bottom of the eighth when Pena, pinch-hitting with a runner at second and two outs, hit a sharp grounder that Kinsler couldn't handle, allowing Rich Thompson to score.