With the point, New England (2-3-2, 8 points) moved into a tie for sixth place in the Eastern Conference with Atlanta FC.
San Jose (2-2-3, 9 points) moved a point ahead of Real Salt Lake in fifth place in the Western Conference.
New England saw a six-game home winning streak end. The Revolution had a 15-8 edge in shots, including a 6-3 advantage in shots on goal.
San Jose has now gone five straight matches without a win. The Earthquakes opened the season with back-to-back wins, but two of their draws have come off last-minute equalizers.
After an underwhelming first half, San Jose came out hot in the second half, mounting two solid scoring chances in the opening minutes, But Cody Cropper saved the Earthquakes' first shot on goal before Jahmir Hyka's shot sailed over the crossbar.
Neither team could get much momentum in the second half, as the Earthquakes held only a 6-5 edge in shots in the second half.
New England came out fast in the first half, holding nearly 70 percent of the possession in the first 10 minutes but had nothing to show for it. Their best chance may have come in the 31st minute when Kelyn Rowe went up for a header but sailed it just over the crossbar.
In the first half, New England had 10 shots (three on goal). San Jose, which came into the match tied for fifth in MLS at 14 shots per game, had just two.
The Revolution held possession for 57 percent of the half but could not solve David Bingham.