Ibanez's first homer of the game was a two-run shot in the fourth inning that broke a scoreless tie, and he made it 4-2 Yankees with a bases-empty blast in the seventh.
Curtis Granderson hit his 10th home run of the year for New York, which clinched its three-game series against the Rays.
Ivan Nova (4-1) collected the victory, yielding a pair of runs on six hits while walking two and striking out eight.
James Shields (5-1) was saddled with his first loss in seven starts to begin the season, surrendering three runs on four hits in a six-inning effort.
Notable deaths of 2014 [PHOTOS]