Pruitt split time between the majors and Triple-A over the last three seasons. He posted a 4.40 ERA, 1.25 WHIP and 39 strikeouts in 47 innings (14 appearances) with the Rays last season, making two starts.
The 30-year-old Pruitt, who is out of minor-league options, can serve as either a starter or reliever, throwing at least five innings in five of his 14 appearances in 2019. Astros general manager Jeff Luhnow believes Pruitt can compete for a back end of the rotation spot.
"We’re going to give him a chance to compete," Luhnow said, according to Brian McTaggart of MLB.com. "He's started in his Major League career, so he's capable. He's got two different breaking balls, a good fastball and really good command, which means he should be able to get through some innings."
Tampa Bay gets a pair of prospects to add to a deep system, though neither were ranked in Houston's top 30.
Battenfield, 22, was selected in the ninth round of the 2019 draft. He posted a 1.60 ERA, 0.97 WHIP and 46 strikeouts in 39 1/3 innings in A-Ball.
Stevenson was a 10th round pick by the Toronto Blue Jays in 2018 and was packaged to Houston along with Joe Biagini and Aaron Sanchez at last year's trade deadline for Derek Fisher. The 23-year-old hit .288/.388/.384 with five home runs, 15 doubles and 13 stolen bases in 113 games in A-Ball in 2019.
The deal marks the second of the day for Tampa Bay, who also sent pitching prospect Matthew Liberatore to the St. Louis Cardinals for first baseman Jose Martinez and outfielder Randy Arozarena.