Tampa Bay won for the third time in four games this season, holding the Yankees in check after Alex Rodriguez had given them an early lead with a two-run triple.
That hit came in the top of the fourth, but the Rays immediately responded with a five-run inning that featured Pena's two-run blast. Jason Bartlett also doubled home two runs in the Tampa Bay fourth.
Aybar's homer came in the sixth inning, after which Carl Crawford singled in a run and Ben Zobrist added a run-scoring double.
David Price (1-0) got the victory, giving up three runs on seven hits while striking out seven over 7 2/3 innings. He threw 111 pitches.
Javier Vasquez (0-1) surrendered eight runs on eight hits over 5 2/3 to take the loss.