Jones's 10th homer this season gave Texas a 3-0 lead with one out in the bottom of the first. He added an RBI double in the sixth.
Nelson Cruz had three hits, one a fifth-inning solo homer, and two RBI. Taylor Teagarden added two hits and two RBI and Marlon Byrd scored three times for the Rangers, who have won four straight and can sweep the series Sunday.
Starter Derek Holland (2-5) got the win despite giving up four runs on seven hits with one walk and four strikeouts.
Dioner Navarro led Tampa Bay with two hits -- one a three-run homer in the fifth.
Tampa Bay starter David Price (2-3) lasted just 1 1/3 innings, allowing six runs on just three hits with five walks and three strikeouts.