Alfonso Soriano had three hits and a career-high five RBI as the Rangers ended the Devil Rays' season-best six-game winning streak with a 13-5 victory.
Hank Blalock hit a two-run homer and Phil Nevin added a solo shot in a decisive three-run seventh for the Rangers, who scored 12 runs in the last three innings.
"It's so easy to get in that here-we-go-again mindset if you let it," Rangers manager Buck Showalter said. "It's just good to win a game and have the guys look at a cup half full instead of half empty."
Tampa Bay had taken a 5-4 lead in the top of the seventh on Toby Hall's RBI double, and Devil Rays reliever Chad Orvella (1-2) got the first two outs in the bottom of the inning.
But Nevin, who had three hits and fell a triple short of hitting for the cycle, tied it with his first homer since being acquired last week in a trade with the San Diego Padres.
"No matter how long you play, you want to make a good impression and do something right away," said Nevin, who was 1-for-12 in his first three games with the Rangers. "I'm getting more comfortable with the (DH) role. It's something I'm going to have to get more accustomed to."
Soriano then reached first when Orvella was charged with an error on a high throw to first after fielding a bunt. It was the fifth time Soriano reached base safely.
Blalock followed with his 21st homer to put the Rangers in front 7-5.
Michael Young, who had three hits, had a three-run homer in the eighth to make it 10-5. Soriano added a two-run double and Blalock, who had three hits, had an RBI single in the eighth.
All six runs in the eighth came off Dewon Brazelton, who walked five in the inning.
"I'm not terribly concerned, but I'm certainly not pleased with the way it went," said Brazelton, who faced 12 batters in the eighth and threw 46 pitches -- only 17 for strikes.
Kevin Gryboski (1-0) allowed one run and two hits in two-thirds of an inning for his first AL victory.
Orvella allowed three runs -- one earned -- and two hits in one inning.
Texas ended a seven-game home losing streak, its longest at Ameriquest Field. The club record for consecutive home defeats is nine in 1990 when the Rangers played at Arlington Stadium.
"We did hit a tough stretch at home but that's something that's very rare for us," Young said. "Regardless of wins and losses, we feel comfortable playing here. It's good to finally win here and get on a good stretch."
Aubrey Huff homered and Carl Crawford had three hits for the Devil Rays. Tampa Bay's winning streak was its best since a 12-game run from June 9-22, 2004.
"Overall, we're happy. I'm not complaining," Devil Rays manager Lou Piniella said as the team prepared for a flight to the West Coast for a three-game series against the Los Angeles Angels. "You'll take two out of three anywhere you go. Now we've got to go to California and try to get another win streak going."
The Devil Rays took a 4-1 lead into the sixth behind starter Casey Fossum.
But Texas used a three-run sixth to draw even on Soriano's two-run triple and Blalock's RBI single, knocking out Fossum.
Fossum allowed four runs -- three earned -- and eight hits in 5 1/3 innings.
Texas starter Joaquin Benoit allowed four runs and nine hits over 5 1/3 innings.
Huff led off the second with his 14th homer, hitting an 0-2 pitch into the upper deck in right. Tampa Bay made it 2-0 in the third on Jorge Cantu's RBI single.
The Rangers cut the deficit to 2-1 in the fourth on Soriano's RBI single.
The Devil Rays made it 3-1 in the fifth on Huff's RBI single, and Crawford's run-scoring single in the sixth pushed the lead to 4-1.