Wegner's tally in the 44th minute came off a set piece in which Justin Mapp found Patrice Bernier on a corner kick and he in turn crossed to Wenger. The Impact striker then headed the ball past Zac MacMath for his fourth of the season.
Montreal (10-13-3) doubled its advantage in the 78th on a Felipe Martins score off a Hassoun Camara cross.
The Impact's win put them two points out of the final playoff spot in the Eastern Conference.
The Union fell to 7-12-2 with the setback.