Rangers second baseman Joaquin Arias couldn't track down B.J. Upton's one-out bloop double that started the Rays' late rally. Bartlett reached on an infield single and easily beat Arias' throw to second on Carl Crawford's fielder's choice grounder.
"We didn't catch the popup, we didn't get the out when we should have got it," Rangers manager Ron Washington said. "There were too many outs that were supposed to be outs that didn't happen and that was the game right there."
Tampa Bay moved into a tie for first place in the AL East with the New York Yankees, who lost 3-1 to Detroit. The Rays own a 5 1/2-game cushion in the wild-card standings.
"It was kind of a nice win, wasn't it?" Rays manager Joe Maddon said. "Throughout all that good stuff, the one thing I really want to point out is Jason Bartlett beating the force play at second. That was the biggest event for us to win that baseball game."
Lee outlasted David Price in a marquee matchup of All-Star aces and was given a late lead when Texas scored twice in the top of the eighth to go up 4-2. But Crawford hit a run-scoring grounder and Evan Longoria tied it with a single before Pena, just off the disabled list, made it 5-4.
Ben Zobrist added an RBI single that chased Lee (10-6).
"It was kind of a blur of an inning," Lee said. "Things kind of fell apart. I don't know why. It was a strange inning."
The left-hander allowed six runs, nine hits and one walk while striking out 10 over 7 2/3 innings. He has lost all three of his starts against Tampa Bay this season.
Price got a no-decision in his bid to become the AL's first 16-game winner, giving up two runs and five hits in six-plus innings. The hard-throwing lefty struck out eight and walked five.
The matchup between Lee and Price marked the first time two pitchers with 10 or more wins and ERAs under 3.00 faced each other at Tropicana Field, which opened in 1998. The announced crowd was just 18,319 for the opener of a three-game series.
Texas has an eight-game lead in the AL West.
Rangers third baseman Michael Young left after six innings with neck stiffness and will have his playing status evaluated Tuesday. Young first felt the discomfort when he woke up Monday.
Pena drew just the 10th walk -- and first to a left-handed hitter -- issued this season by Lee, and Sean Rodriguez singled in the fifth. Willy Aybar later put the Rays up 2-0 on a bloop single to right over a drawn-in infield.
Lee retired 11 in a row before Crawford singled with two outs in the fourth.
Molina had a strange leadoff double during a two-run seventh that resulted in a 57-second delay for an umpire review. Crawford tried to climb the left-field fence in what appeared to be an attempt to take away a homer, but ended up about 10 feet away from where the ball hit off the wall.
David Murphy ended Price's night with walk before Chad Qualls loaded the bases with another walk to Brandon Boggs. After a run scored on pinch-hitter Mitch Moreland's double play, Elvis Andrus tied it at 2 with an RBI infield single.
Price worked out of a bases-loaded, two-out jam in the sixth by striking out Jorge Cantu. Guerrero had an infield single to second in the inning that hit Rodriguez just below the collarbone and then got briefly lodged in the infielder's uniform.
"I was just trying to make sure I kept it in front of me knowing that there's a guy on second at the time," said Rodriguez, who still had a red spot after the game from where the ball struck him. "Sure enough it hit me. I looked down and could see it was rolling down my shirt. It's frustrating, but Price struck out the next guy."
Texas put OF Nelson Cruz (strained left hamstring) on the 15-day disabled list and reinstated Arias (strained back muscle) from the 15-day DL. ... Tampa Bay reinstated Pena (sore right foot) from the 15-day disabled list and placed OF Gabe Kapler on the 15-day DL with a sprained right ankle. ... Rangers INF Ian Kinsler (strained left groin) is set to resume baseball drills this week. ... Tampa Bay RHPs Jeff Niemann and Wade Davis, both out with strained right shoulders, are expected to pitch in simulated games Friday and could rejoin the rotation next week. ... Rangers RHP Rich Harden (right shoulder tendinitis) is scheduled to make a start for Triple-A Oklahoma City on Tuesday.