Stairs's moon shot to right field, the final blow in a fluctuating contest, came just three at-bats after Shane Victorino's game-tying two-run homer for the Phillies.
The teams combined to use 13 pitchers with Philadelphia's Brad Lidge retiring Los Angeles for the final four outs.
Dodgers third baseman Casey Blake hit a solo home run in the sixth in which the Dodgers scored twice to take a 5-3 lead but were unable to hold on to it with their bullpen.
Game Five in the best-of-seven series is on Wednesday at Dodger Stadium.










