Mwanga scored in the 73rd minute, 14 minutes after Jeff Larentowicz opened the scoring for Colorado.
Philadelphia (4-10-5) settled for its second straight draw at home and slipped to 0-1-3 in its last four matches in the newly-built stadium in Chester, Pa.
Colorado (7-5-7) failed to build on a win over San Jose last weekend, which is the Rapids’ lone win in its last nine matches.
After a slow first 30 minutes, the Union’s Alejandro Moreno hit the right post in the 30th minute as he came within inches of his second goal of the season.
Union leading scorer Sebastien Le Toux fired wide left late in the first half, as Philadelphia failed to convert the best two chances in the opening half.
Philadelphia had another chance early in the second half when Mwanga set up Le Toux, but he missed wide left again with his 10th goal of the season in sight.
Colorado converted its first good chance 15 minutes into the second half, when Larentwoicz latched onto a ball just outside the box and drilled a shot inside the right post in the 59th minute for his second goal of the season.
Le Toux turned provider just under 15 minutes later when he ran onto a pass in the left side of the area, held off Colorado defender Marvell Wynne, and found Mwanga in the middle of the area.
Mwanga controlled the ball well with his first touch, then poked the ball past Colorado goalie Matt Pickens from close range. Mwanga, the No. 1 pick in the MLS draft, scored in his second straight match and has all of his goals in his last 11 games.
Pablo Mastroeni wasted a golden chance for Colorado to escape with a road win, as he fired wide right from the edge of the area in the 81st minute.
Philadelphia had two chances in stoppage time to earn its fourth home win, but Le Toux had a penalty appeal denied after he was fouled in the box in the 92nd and Michael Orozco Fiscal had a late goal called back for offside.
Colorado visits the Columbus Crew on Aug. 21 in its next game, while the Union take a five-game winless skid to D.C. United on Aug. 22 for their next match.