The game was scoreless until the 75th minute, when McInerney tallied off a set piece started by Sebastien Le Toux.
On the winning play, McInerney headed a Le Toux corner kick toward the goal. An initial save was made by Revolution goalkeeper Bobby Shuttleworth but McInerney scored on the rebound for the Union (2-1-0).
Philadelphia improved to 5-0-3 all-time against the Revolution.
Jerry Bengston had the best chance for New England (1-1-0) in the 35th minute, but Zac MacMath was equal to the task with a kick save.