Tampa Bay produced 14 hits in support of Jeremy Hellickson (8-3), who struck out nine and gave up a lone run on six hits while throwing 100 pitches in seven innings.
The Rays took control in the second with Molina hitting a two-run homer and Johnson delivering a solo shot. Evan Longoria singled in another run in the inning and later scored on a double by Wil Myers.
Chicago starter Dylan Axelrod (3-5) recorded only five outs as he was giving up five runs on nine hits.
The Rays have won two straight and six out of seven.
Celebrity Breakups and divorces of 2014 [PHOTOS]