The Twins rookie right-hander threw five pitches in the first inning before he endured a rain delay of 1 hour, 26 minutes. Manager Ron Gardenhire said he normally would replace a starter after that lengthy of a break.
Instead, De Vries (3-5) was sent back to the mound. He responded by allowing two runs and three singles in five innings against the high-powered Rangers.
"I was pretty much 100 percent sure that it wasn't going to happen because our bullpen has just been killed the past couple of days," said De Vries, who threw 98 pitches. "So I had to go out there and eat up as many innings as I could."
De Vries was 0-4 in 10 starts since beating Kansas City on June 30. Included in that drought was a tough-luck start against the Rangers on July 8 where he pitched seven shutout innings before his bullpen blew a lead.
"I'm happy to have a performance like that against a powerful offense," De Vries said.
The Twins avoided getting swept in the four-game series. They finished a 10-game road trip with a 2-8 record.
Revere lined an RBI triple in the sixth that gave the Twins a 6-2 lead. The speedy right fielder reached base five times and scored three runs.
"We finally got one to go our way," Revere said. "We're a good enough team that we should be able to compete with these guys."
Josh Hamilton hit his 35th homer for Texas and drove in four runs, giving him a major league-leading 111 RBIs.
Scott Feldman (6-10) lost his fourth straight start. He gave up six runs and 10 hits in 5 2/3 innings.
"I made good pitches," Feldman said. "That's the frustrating thing about it."
Texas jumped on De Vries after the rain delay.
The AL West leaders got three straight singles after play resumed, capped by Hamilton's two-run hit that put Texas on top 2-1.
De Vries retired 15 of the next 16 he faced. The only batter to reach was Geovany Soto, who struck out but got to first on a passed ball.
Minnesota's starting pitching had been battered in the first three games of the series, giving up 18 earned runs and 24 hits in 9 2/3 innings.
"We can score some runs," Gardenhire said. "We just need an opportunity to stay in games."
The Twins a took the lead for good with an unearned run in the third as first baseman Mitch Moreland and third baseman Adrian Beltre committed errors. Justin Morneau's sacrifice fly to shallow left, which Hamilton dropped while transferring the ball from his glove, put the Twins ahead 3-2.
Mauer and Trevor Plouffe had RBI singles in the fifth that extended Minnesota's lead to 5-2.
Twins LHP Scott Diamond said he is ready to make his scheduled start Tuesday as he awaits word on his appeal of a six-game suspension for a pitch thrown near the Hamilton's head. Diamond said the appeal was filed late Friday afternoon and was uncertain whether the league would address it by Monday. "I don't know when I will hear," Diamond said. "It might take them a day or two." ... The Tampa Bay Rays announced that RHP Alex Cobb will start against the Rangers on Wednesday. ... Gentry ran into 2B Ian Kinsler making a catch to end the fifth. Gentry was down for a couple of minutes, but walked off on his own and remained in the game.