The win was the first ever at RFK Stadium for the Union, who had been 0-1-2 there. The Union are 2-1-1 on the road this season after going 3-10-4 away from home last year.
"I think we have matured and we are tougher now, and I like us that way," team manager John Hackworth said.
Part of that toughness comes from forward Conor Casey, who is among the most difficult players in MLS to push off the ball. He and McInerney are developing good chemistry.
"I think it's even going to get better as we continue to play together," Casey said.
McInerney got things started by scoring in the seventh minute. Taking a long pass from Casey, he dribbled through defenders Brandon McDonald and Dejan Jakovic and buried a shot from just inside the box.
Casey connected in the 11th minute. The goal was set up by former United midfielder Danny Cruz, who dribbled down the right flank, cut the ball back, and found Casey at the top of the box. The Union forward drilled it past United keeper Bill Hamid.
United cut the lead to 2-1 in the 17th minute when McDonald crossed the ball from the left wing to the far post to Dwayne De Rosario. De Rosario made a back pass to a charging Perry Kitchen, who shot from about 8 yards, just ahead of a sliding Amobi Okugo.
McInerney scored his second goal in the 26th minute on Sheanon Williams' long throw into the box. The throw was glanced on an Okugo header to McInerney, who sent a left-footer from about 12 yards out into the bottom right corner.
United made it 3-2 when Lionard Pajoy, who was traded by the Union last year for Cruz, headed in a long cross from Daniel Woolard in the 47th minute.
In stoppage time, Union keeper Zac MacMath stopped a 25-yard free kick by former Union forward Carlos Ruiz that had plenty of force in what would be United's final scoring chance.
Contact Marc Narducci at firstname.lastname@example.org. Follow on Twitter @sjnard.