Tom Gordon (0-2), working his second inning of the game, retired the first two batters in the 12th before Reyes doubled to center.
Pagan then lined a shot that bounced off the mound and up the middle. The throw home by centerfielder Jayson Werth was on target, but Reyes just beat the tag.
Jorge Sosa (1-0) got the final out in the top of the 12th for the win. Starter John Maine, who has won all four of his decisions against the Phillies, allowed one run on five hits over six innings.