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Union will take on Supporters' Shield winner LAFC in the season decider on 5 November at Bank of California Stadium, with Steve Cherundolo's side easily accounting for Austin 3-0 earlier in the day.
Philadelphia had lost to NYC in last year's Conference Finals but a burst of goals from Julian Carranza, Daniel Gazdag and substitute Cory Burke sent it into its first-ever MLS Cup.
NYC had silenced the Subaru Park crowd when it went ahead in the 57th minute from Maxi Moralez's low strike after a cushioned pass from Santiago Rodriguez.
MLS Goalkeeper of the Year Andre Blake prevented a second NYC goal when he made a one-handed save to deny Alexander Callens' header.
Union capitalized on Blake's brilliance almost immediately, with Carranza slotting in a 65th-minute equaliser from Jakob Glesnes' quickly-taken free-kick.
Two minutes later Jack McGlynn's brilliant cross-field ball was headed down expertly by Carranza, splitting two defenders and setting up Gazdag to fire home for 2-1.
Burke, who had been brought on in the 62nd minute, burst forward with speed and strength to lash in a left-foot strike for 3-1 in the 76th minute.
LAFC's win over Austin was less complicated, with Cristian Arango nodding it ahead in the 29th minute, before a second-half Maximiliano Urruti own goal and Kwadwo Opoku strike settled its Conference Final.
Philadelphia and LAFC had both been top seeds in the Eastern and Western Conferences respectively, having finished the regular season equal on points.
LAFC won the Supporters' Shield due to recording more wins across the regular season. Both clubs will be aiming for their first-ever MLS Cup titles.