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.