The game was scoreless in the first half when Goncalves drilled home a volley from the back post off a pass from Juan Agudelo for his second goal of the season.
The victory gave the Revolution (13-11-9) 45 points, which at least temporarily put them into post-season position with the fifth spot in the Eastern Conference.
The Impact (13-12-7) remained in the East's playoff picture despite the loss, holding onto fourth place with 46 points.
Astronomers offer more expansive view of universe
Beautician charged with giving client fatal silicone butt injection