United States forward Donovan had twice got the Galaxy back on level terms, firstly by neatly notching from Robbie Keane's pass in first-half stoppage time to cancel out Matt Hedges' headed opener - Dallas' first goal in 464 minutes - and then in the 73rd minute after Perez had toe-poked past Carlo Cudicini to edge the hosts ahead for a second time.
Donovan looked to have clinched the points for the visitors when he pounced on a loose ball and coolly slotted home to complete his treble eight minutes from time, but Perez's sweet volley four minutes later ensured the shares were spoiled.
The draw meant the Galaxy remained fifth in the Western Conference, while Dallas stayed outside the play-off positions in seventh.
In Sunday's other game, substitute Martin Rivero equalised 10 minutes from time to earn the 10-man Colorado Rapids a 1-1 draw against nine-man Chivas USA.
Carlos Alvarez's slick left-footed finish had opened the scoring at the StubHub Center for bottom-placed Chivas, who lost Gabriel Farfan to a red card for a foul on Shane O'Neill 12 minutes before the interval.
Two more dismissals followed after the break, Colorado midfielder Tony Cascio evening up the numbers briefly before Chivas' Tristan Bowen joined him in heading for an early bath after spitting in the direction of Rapids defender Chris Klute.
And the third-placed visitors made their man advantage tell in the final half-hour as Rivero's superb header secured a point for his side.