Jack McInerney wasted a good opportunity to put the visitors ahead after being slipped through by Conor Casey in the 12th minute, but it was the Union who took the lead through Shea Salinas three minutes later.
John Hackworth's men threatened once more in the 25th minute, but Chris Wondolowski saw his effort cleared off the line.
The Earthquakes remained one in front at the break, but the Union came close to equalising when Keon Daniel clattered a shot off the post four minutes after the restart.
The hosts were reduced to 10 men just before the hour mark when Rafael Baca picked up his second yellow card for a foul on Casey.
However, it did not affect the outcome as Mark Watson's team held on to draw level on points with seventh-placed Vancouver Whitecaps in the MLS Western Conference.
Meanwhile, the Union remain fourth in the Eastern Conference, six points behind the leading trio of Montreal Impact, New York Red Bulls and Sporting Kansas City.