Chivas defender Josue Soto earned his second yellow card after playing the ball back to the goalkeeper. That set up the indirect kick. Moments earlier, Union team manager John Hackworth had been sent off after arguing for a handball.
The Union snapped a three-game winless streak and extended Chivas' own dismal streak to 14 games. The Union are now tied for second place in the Eastern Conference with 30 points.
Driving rain turned the match into a battle to stay upright.
"Usually the rain doesn't affect a soccer game as much as it did tonight," Hackworth said. "The field was so saturated."
Players fell in the box and they fell at midfield. They fell on their chests and slid for yards. For the Union, one fell at the worst possible time.
In the 14th minute Amobi Okugo slipped in the box while marking Jorge Villafaña. Suddenly alone, Villafaña slid a pass to Jose Correa who tapped in the easy goal.
The Union evened the match in the 58th minute when Brian Carroll deflected a Conor Casey header. Casey also tapped in a goal in the 89th minute.
The Union once again played without forward Jack McInerney and midfielder Keon Daniel, who have missed action while playing in the Gold Cup.
The match slipped into disorder in the 77th minute with Hackworth's ejection. The yellow card minutes later delayed play for several minutes as Chivas hounded referee Jorge Gonzalez. Through it all, Farfan stared down the goal.
It's not something that's practiced, Union goalkeeper Zac MacMath said, "because it happens so infrequently. So that's something you just - playground ball stuff."
"We knew they were going to have pretty much their whole team in the goal," Farfan said.
Sebastien Le Toux tapped Farfan the pass, and he shot over the wall of defenders.
Notes: Toronto FC defender and former Union captain Danny Califf announced his retirement Friday. Califf was an original member of the Union and played for three seasons.
Contact Zach Helfand at firstname.lastname@example.org. Follow on Twitter @zhelfand.