Carlos Ruiz and Veljko Paunovic also scored in the second half for the Union (7-4-5), who took sole possession of first place in the Eastern Conference while snapping a four-game winless streak. Philadelphia remained undefeated at home, improving to 5-0-4.
Michael Umana and Justin Braun scored for Chivas (4-7-5), which dropped its third straight.
Ruiz's goal from 8 yards out in the 68th minute put the Union up 2-1, but Braun answered 9 minutes later.
Mwanga, who missed Union's scoreless draw against Sporting Kansas City on Wednesday night because of a knee injury, took a cross from Sebastien Le Toux and rifled it low and into the right side of the net past diving goalkeeper Dan Kennedy.
Chivas USA opened the scoring in the 27th minute when Umana scored on a header from close range off an assist from Ben Zemanski. Philadelphia tied it 2:24 into the second when when Paunovic tallied on a volley from 13 yards out.
Ruiz put the Union ahead, taking a long pass from Paunovic just outside the penalty area. Ruiz settled it with his chest, took one dribble and fired a right-footed shot from 8 yards out through Kennedy's legs.
Braun tied it in the 77th minute from 19 yards out, beating hard-charging Union goalkeeper Faryd Mondragon to the ball on a through pass.
(Copyright 2011 Philadelphia Union. Reprinted by permission)