The Crew (5-4-4) extended their unbeaten streak to six matches (3-0-3) overall and five (3-0-2) against the Revolution.
Matt Reis had three saves for New England (5-7-2), getting his third shoutout of the season and 58th of his career. The Revolution had scored in six straight matches and totaled 12 goals in their previous six at home, but were shut out for the fifth time this season.
New England had some scoring chances in the first half, but Benny Feilhaber missed in the opening minute and Gruenebaum smothered Jose Moreno's solo breakaway attempt from the left side in the 15th. Saer Sene laced an 18-yard blast off the crossbar in the 29th minute and Fernado Cardenas had a shot off the right wing and a rebound in the 38th.
In the second half, Kelyn Rowe (72nd) and Lee Nguyen (90th) had shots knocked away by Gruenebaum.
Reis made a diving stave on Milovan Morosevic's drive in the eighth minute, and Morosevic had drive off the crossbar in stoppage time.