In the sixth, Wil Myers singled with two outs then stole second before scoring on Scott's hit.
"They're little things that mount up in the course of a game, and I think that's indicative of what we've been doing as a lineup," Scott said. "Guys up and down the lineup contributing all sorts of things with the bat, with the legs."
After Scott's eighth homer got the Rays on the board, Escobar doubled with two outs and stole third base on a very close -- and risky -- play.
"That's got to be almost a 100 percent play if you're going to try that," Rays manager Joe Maddon said. "Why do that? Because then Desmond can do what he did."
Jennings beat out a bunt down the first base line and Escobar scored to make it 3-3.
"The pitcher was lifting his leg and he gave me just one look," Escobar explained through an interpreter. "I thought I could get a jump and get to third base. After that, a wild pitch or anything could score me, so I took a chance."
Roberto Hernandez survived a shaky first inning to post the Rays' 14th straight quality start, going six innings and giving up three runs and six hits. He won for the first time in six starts since June 11. Hernandez (5-10) struck out six.
Myers had two hits and scored twice for the Rays, who have won 13 of 15. Fernando Rodney pitched the ninth for his 22nd save.
The Astros jumped out to a 3-0 lead behind Brett Wallace's two-run homer and J.D. Martinez's RBI groundout. Houston had four hits in the first but only two the rest of the way and never got a runner to second base in the final eight innings.
The Rays tied it in the fifth against Keuchel, who gave up six hits and three runs in 5 1/3 innings. Scott's single in the sixth came off Lucas Harrell (5-10), who relieved with one out.
"When you're called on, you have to go up there and get people out," Harrell said. "It doesn't matter what the situation is, you have to go out there and make pitches."
Scott, who extended his hitting streak to nine games, is hitting .373 with five home runs in his last 23 games.
"I've had some moments in my career like this and even better, where the baseball slows down for me and the swing feels good and I'm not missing the pitches I've been getting to hit," he said. "It's familiar territory, but it's been a long time and I'm enjoying it."
Rays RHP Alex Cobb is scheduled to pitch batting practice Sunday for the first time since being struck on the ear by a line drive on June 15. Cobb, who has had three bullpen sessions since his concussion, is hopeful of a return in early August. ... The Rays announced that David Price, Jeremy Hellickson and Chris Archer will pitch their first three games after the All-Star break in Toronto. All-Star Matt Moore will pitch at Boston on July 22, followed by Hernandez the next day. ... The Astros activated OF Justin Maxwell, who sustained a concussion on June 25. Maxwell took the roster spot of RHP Jarred Cosart, who won his major league debut here Friday night. ... Carlos Pena, the all-time home run leader at Tropicana Field with 86, led off for Houston for the first time.
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ST. PETERSBURG, FL - JULY 13: Pitcher Dallas Keuchel #60 of the Houston Astros pitches against the Tampa Bay Rays...