The 22-year-old went 3-for-4 at the plate and cranked his first career home run, raising his average from .057 to .128.
The ball was crushed to left field off reliever J.P. Howell in the ninth inning, giving Boston a 4-1 lead and nearly putting the game out of reach before Tampa Bay rallied in the bottom of the frame.
His other two hits were both singles off Rays ace David Price, eventually scoring on one of them.
"He had real good batting practice today, was very aggressive in batting practice and took it right into the game," manager Bobby Valentine said. "He swung at the first pitch twice and got a couple of singles. He swung hard and hit one out of the park."
Valentine added that Iglesias appears to be having a better approach at the dish.
"It seems like every game his confidence has been building, getting walks and having better at-bats," said Valentine, who before the game said Iglesias will see regular playing time as the season draws to a close.