Ben Zobrist added an RBI single that chased Lee (10-6).
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 while Tampa Bay began the night a game behind the first-place New York Yankees in the AL East. The Rays own a 5 1/2-game cushion in the wild-card standings.
Rangers third baseman Michael Young left after six innings with neck stiffness. Young first felt the discomfort when he woke up Monday.
Lance Cormier (4-3) got the final out in the eighth before Rafael Soriano pitched the ninth for his 34th save.
Texas scored twice in the eighth for a 4-2 lead. Joaquin Arias tripled and scored when Vladimir Guerrero hit into a double play. Bengie Molina added an RBI single.
Pena drew just the 10th walk 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 15 feet away from where the ball hit off the wall.