Philadelphia erased a 1-0 deficit in the 59th minute on a penalty kick goal from Freddy Adu after defender Kevin Alston was ruled to have brought down McInerney in the box.
Then, with time ticking down, Sheanon Williams sent a cross through the 6-yard box to the left post, where McInerney sneaked behind Alston and headed it across the goal line in the 90th minute.
The Union (7-10-2) improved to 5-2-0 in their last seven games, using the win to pull even with the Revolution (6-10-5) for eighth place in the Eastern Conference.
Saer Sene scored his ninth goal of the season in the first half for New England.
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