Napoli drilled the first pitch after the delay high off the wall in left field and Pedroia scored easily.
Both starting pitchers performed well. Tampa Bay's Jeremy Hellickson allowed three hits, including a first-inning triple to Jacoby Ellsbury that led to a run and a fifth-inning home run by Jarrod Saltalamacchia. Hellickson walked one and struck out nine in seven innings.
Boston starter Ryan Dempster gave up just two hits -- one Evan Longoria's first home run of the season -- while walking two and striking out 10 in seven innings. He had 25 strikeouts in 17 innings this season.
Dempster left the game with a 2-1 lead but the Rays reached reliever Andrew Bailey for a tying run. Desmond Jennings singled to open the inning and took second for his fourth stolen base of the season. Ben Zobrist followed with a single to left that scored Jennings.
Bailey (1-0) still came away with the win as Boston scored in the bottom of the inning.
The Red Sox swept the three-game series, allowing the Rays just 13 hits and three runs.