Mapp's first goal came in the 11th minute, picking out the bottom right corner of the net and beating Toronto FC goalkeeper Stefan Frei from 25 yards for a 2-0 lead.
His second tally put the Union ahead 4-2 in the 62nd minute, only 3 minutes after the second of Maicon Santos' two goals had brought Toronto to within a single score.
Mwanga added a pair of tallies late in the game to pad the advantage while Gabriel Farfan and Kyle Nakazawa also found the net for the Union (6-3-2), who lead the Eastern Conference with 20 points.
Toronto (2-5-6), meanwhile, has managed only one win in 11 games.
2014: The Year in Music [PHOTOS]