Italy started quietly, and didn't carve out a clear chance until Pelle headed Andrea Pirlo's corner inches over the top of goal on 20 minutes.
However, it was Alfred Effiong that almost got his name on the scoresheet first when he charged forward and curled an effort narrowly wide of goal.
The hosts finished the first half the stronger side, though, and could have been ahead when Eder's mazy run ended with a shot that flew just wide of goal.
Pirlo's clever free kick teed up Matteo Darmian shortly after the restart, and the Manchester United defender's cross was almost bundled home by the Sampdoria forward.
Pelle then got the goal his side needed when he turned home substitute Antonio Candreva's cross from close range.
The result leaves Italy with 15 points from their seven games in Group H.