Lenhart erased a 1-0 San Jose deficit with two first-half goals, one in the 15th minute and the second only 7 minutes later when he fired in the rebound of a Khari Stephenson shot.
After rookie Blake Brettschneider scored his first MLS goal in the 34th minute to forge a 2-2 tie for D.C., it was Dawkins who gave the Quakes (5-4-4) the lead for good.
He took a feed from Lenhart and boomed a shot into the left corner for his fourth goal of the season in the 49th minute.
Lenhart then notched his hat trick with another marker in the 60th minute.
Andy Najar also scored for D.C. United (4-5-4).