New England’s Teal Bunbury opened the scoring in the fifth minute with an easy tap in of Scott Caldwell's cross.
The Galaxy's Maganto one-touched a loose ball for a goal in the 18th minute, and Zardes slotted home Jose Villarreal's back-heel pass in the 27th.
Revolution forward Diego Fagundez bent in a free kick over the wall in the 37th minute for the equalizer.
New England is unbeaten in eight straight MLS home games this season, while the Galaxy is winless in its last 14 away matches.
“I'm very happy,” Zardes said after the Galaxy tied the Eastern Conference's second-place team. “It's unfortunate that we didn't get the win but we came out with a point and that's what matters.”
U.S. international Jermaine Jones left in the 33rd minute because of a left groin injury. He stood and signaled to the bench for medical help before going to the ground. He was able to slowly walk off under his own power.
Meanwhile, Zardes and Jones were among 22 players called up Sunday to the U.S. national team by Coach Juergen Klinsmann ahead of Friday’s friendly with the Netherlands in Amsterdam and next week’s game against World Cup champion Germany in Cologne.
They were among nine players to be summoned off MLS rosters. Zardes’ Galaxy teammate Omar Gonzalez, who started against Germany in last summer’s World Cup, was not among them. The call-up was the fourth this year for the 23-year-old Zardes, who earned his first career assist in a 2-0 win over Panama in February.