The Rays took a 13-0 lead through three innings and coasted to their sixth win in eight games.
After Jason Bartlett hit a two-run double in the first inning, Navarro hit a two-run homer in the second and Pena soon followed with a three-run shot.
Gabe Gross had four RBI and contributed a two-run homer in the seventh.
Andy Sonnanstine (3-4) was the beneficiary of the onslaught, getting the win by allowing a run on five hits over six innings. He also scored twice.
Ricky Nolasco (2-50 lasted two innings while giving up eight runs on eight hits. Miami has lost five of six.
Tampa Bay equaled the most runs it has scored in a game this season, having also come up with 15 in a win over the New York Yankees in April.