Earthquakes defender Nathan was sent off after 21 minutes following a video review, turning the game after San Jose had taken the lead via an own goal created by pressure from Cristian Espinosa.
Shortly after Nathan's dismissal, Wil Trapp pulled Minnesota (7-6-6, 27 points) even with his first MLS goal since 2018.
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But J.T. Marcinkowski made two saves to make sure San Jose (5-7-8, 23 points) ran its unbeaten run to nine matches, although seven of those are draws.
United outshot San Jose 15-4 and held 65 percent of the possession but rarely seriously troubled Marcinkowski's goal after pulling level.
All-time MLS leading scorer Chris Wondolowski came on in the 86th minute for his 400th career appearance, becoming the seventh player in league history to accomplish the feat.
The Quakes took the lead after 12 minutes when Espinoza brought down a diagonal ball on the right flank, got down the right and drove in a low cross toward the near post that caromed off Bakaye Dibassy and past goalkeeper Tyler Miller.
But the match tilted in Minnesota's favor a few minutes later when Nathan tried make up for a heavy touch with a sliding challenge meant to win back the ball from Dibassy.
Instead, he caught Dibassy's shin with a studs-up challenge that drew an immediate yellow card from match referee Victor Rivas. After a video review, Rivas determined he had been too lenient and issued Nathan a straight red.
In the immediate aftermath of Nathan's dismissal, Emanuel Reynoso drove a cross toward the back post. Ethan Finlay reached it and found Adrien Hunou inside the area, and Hunou laid the ball back for Trapp to drive low and inside the left post.
Wil Trapp's equalizer secures draw for Minnesota United FC
Wil Trapp finds the back of the net for Minnesota United FC to bring them even with San Jose at 1-1.
San Jose grabs lead on own goal
Minnesota United FC's Bakaye Dibassy is in the wrong place as he deflects San Jose's Cristian Espinoza cross into the back of the net.