Ricketts preserved the tie with a diving save on Jack McInerney from just outside the box in the 89th minute.
McInerney had another chance in stoppage time, but his head ball went wide.
Mwanga, Roger Torres, and McInerney were inserted in the second half, and each gave the Union's offense some much-needed life.
Up until Mwanga's goal, it appeared as if the Galaxy would sneak out of town with a win.
With one star given the night off, the other took over for the Galaxy. Landon Donovan continued his torrid scoring spree to give Los Angeles a 1-0 first-half lead.
Galaxy midfielder David Beckham had the game off. With three games in an eight-day period ending Saturday in Los Angeles against Sporting Kansas City, Galaxy coach Bruce Arena decided to leave the 36-year-old Beckham home to rest.
The Union wished that Donovan joined him.
Los Angeles struck in the 24th minute when Donovan actually set up his own goal. He made an outstanding heel pass to a streaking Juan Pablo Angel, who took a few dribbles and then fanned on the ball.
Donovan was following the play and got the loose ball, connecting from 12 yards. He has scored the Galaxy's last five goals. It was his fifth of the season in seven games.
After that, the Union started to get some chances. The best came in the 32d minute when Kyle Nakazawa's service was headed wide in front of the goal by Carlos Ruiz.
In addition to Beckham, Union team manager Peter Nowak also missed the game. He was in his native Poland participating in a charity soccer match. Assistant coach John Hackworth ran the team.
All season, the Union have struggled to find any consistency on offense. They have scored six goals in eight games, and never more than one in any Major League Soccer game.
One of the players who was most impressive on offense was outside defender Sheanon Williams, who continually attacked from his outside back position.
Even with the lead, the Galaxy continued to attack. In the 57th minute, Angel missed out on a potential breakaway when he lost control.
A few minutes later, Union goalkeeper Faryd Mondragon made a diving save on Chris Birchall's blast from just inside the box.
In the 67th minute, Mondragon quickly came off his line and slid, beating Angel to the ball.
Ruiz hit the post in the 82d minute, but the play was called offside. It appeared as if it would be the Union's final good scoring chance before Mwanga changed things with his first goal of the season.
Contact staff writer Marc Narducci at 856-779-3225 or email@example.com. Follow him on Twitter at Twitter.com/sjnard.