The U.S. international scored in the 23rd minute on a sharp pass from Gyasi Zardes before equaling the MLS record in the 41st minute with a beautiful chip shot over Chivas goalie Dan Kennedy.
Robbie Keane also scored two goals for the two-time defending champion Galaxy, who ended a four-match winless skid.
"The way we started until the end was very professional, very dominating," Keane said.
While Donovan reached milestones and Keane put on yet another multigoal performance, the game also was a showcase for Zardes, whose runs down the left side caused misery for Chivas' defense, particularly Mario De Luna. The midfielder also scored on a scramble in the box in the 26th minute.
In the other match at Vancouver, Camilo Sanvezzo scored twice in a 2-minute span in the second half to help the home team to a 2-2 draw with Portland to keep their playoff hopes alive. The Timbers missed a chance to move into second place in the West despite extending their unbeaten streak to five games.