Jamie Smith had pulled Colorado even 1-1 with a tally in the 68th minute, taking Deshorn Brown's pass and booting the ball over a leaping Zac MacMath into the corner of the net.
But the Union (1-1-0) mounted a counter-attack only 11 minutes later in which Antoine Hoppenot found McInerney with a through ball and Philadelphia forward put it past Matt Pickens for the decisive score.
Amobi Okugo scored in the 34th minute for the Rapids (0-2-0), who fell in their home opener for the first time in 10 years.
The game was originally scheduled to be played Saturday but was postponed by one day due to a snowstorm.
Swim Week Miami Beach 2014 [PHOTOS]