Ignacio Maganto and Gyasi Zardes scored to give the
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."
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.