Matt Garza stopped a short skid that followed his big night.
"It's great, but the biggest thing is that we won," Garza said.
Garza (12-7) went 0-2 in three starts after throwing Tampa Bay's first no-hitter in a 5-0 victory over Detroit on July 26.
"He fought his delivery a little bit early on, but then he found it," Rays manager Joe Maddon said. "I just thought he was throwing the ball better as the game went deeper. He could have gone farther into that game, there's no question. There was no need to."
Garza, who had 10 strikeouts and two walks, struck out AL batting leader Josh Hamilton with runners on second and third to end the third.
"Garza made us look flat," Texas manager Ron Washington said. "You've got to give credit where credit is due. I didn't think he had his real best stuff, but he made pitches when he had to."
Evan Longoria came within a homer of the cycle and had three RBIs for the Rays, who have won the first two games of the three-game series in a potential playoff matchup. The victory gave Maddon his 400th career win.
Carl Crawford also drove in three runs, including a two-run homer during a five-run seventh that extended the Rays' lead to 10-0. Tampa Bay is tied for first place in the AL East with the New York Yankees, a 6-2 winner over Detroit.
The AL West-leading Rangers remained eight games ahead of the Los Angeles Angels, who were beaten 6-0 by the Boston Red Sox. David Murphy had a run-scoring single in the eighth.
Rangers third baseman Michael Young was out of the lineup due to a stiff neck. He left Monday night's 6-4 loss to the Rays after six innings, but Washington said Young could start Wednesday.
Crawford and Longoria hit consecutive RBI triples, and Carlos Pena drove in a run with a double off Tommy Hunter (9-2) as the Rays took a 3-0 lead in the first. Crawford's triple was the 100th of his career, which made the 29-year-old the youngest player to reach that total since Stan Musial (28 years, 8 months) in 1949.
"It's a real cool thing," Crawford said. "You like to be in the company with guys like that."
Longoria made it 5-0 with a two-run double in the fourth.
Hunter allowed four runs and six hits over three-plus innings. The right-hander was pitching on three days' rest after lasting just three innings in his previous start Friday because of a stomach virus.
Hunter threw 63 of his 83 pitches -- including 38 in the first -- through two innings. He stayed in the game after taking Crawford's second-inning single off his right hand.
"He's healthy," Washington said. "It's one of those nights. He kept the ball out over the plate and they didn't miss it. It happens."
Tampa Bay's Jason Bartlett, running toward second on John Jaso's bunt in the fourth, collided hard with Rangers second baseman Andres Blanco, but both were able to stay in the game.
NOTES: Crawford is the 15th player since 1900 to have at least 100 triples and 400 steals. ... Texas plans to recall LHP Derek Holland from Triple-A Oklahoma City to start Wednesday's game against the Rays. ... OF Josh Sale, the Rays' first pick in the 2010 draft, was at the game. He will report to the team's complex in Port Charlotte later this week and will participate in the Florida instructional league that begins next month. ... RHP Luke Jackson, who agreed to a contract Monday with the Rangers, will join the team's rookie-level club in the Arizona League. He was selected 45th overall in the June draft.