Craig Gentry had four of the Rangers' 16 hits and three of their five stolen bases, the most against the Rays this season.
Andrus' homer was his second of the series and his fourth of the season, all since Aug. 10. Moreland, the only left-handed hitter in the Texas lineup, hit his 23rd and it was No. 17 for Rios. Geovany Soto added his eighth homer off Cesar Ramos in the ninth.
The Rangers were down 2-1 when Moreland led off the third with long drive to left-center. Following Ian Kinsler's flyout to the warning track in left, Andrus and Rios hit consecutive home runs to left.
NOTES: Rays SS Tim Beckham, the first overall pick in the 2008 draft, singled as a pinch hitter in his major league debut. ... Texas OF Nelson Cruz (suspension) has started playing games with the Rangers' instructional league team in Arizona. ... Tampa Bay sent Class-A LHP Matthew Spann to Washington as the player to be named in an August 23 trade in which the Rays obtained OF David DeJesus. ... Rays rookie OF Wil Myers got his first haircut since spring training, which garnered a lot of attention in the clubhouse. "He told me he paid $14 for it, and that's $14 too much," said pitcher David Price. ... Tampa Bay RHP Jesse Crain (right shoulder strain) threw 26 pitches in an instructional league game. The Rays expect to activate him soon.