Rollins drilled a two-run single in the fifth inning to produce a 2-2 tie and added a run-scoring hit in the Phils' five-run eighth, while Polanco scored the go-ahead tally on Shane Victorino's sixth-inning double.
Carlos Ruiz added a pair of RBI for the Phils, who entered the game 2 1/2 games behind first-place Atlanta in the National League East.
Roy Oswalt (8-13) picked up the win, yielding three runs in seven innings, walking none and striking out seven.
Barry Zito (8-7) took the loss for the Giants, who went down for third time in four games and failed to gain ground on first-place San Diego in the NL West.
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