Sporting (11-6-4) moved one point behind first-place New York in the Eastern Conference. Nielsen's shutout moved him one ahead of Vancouver's Joe Cannon.
Matt Reis earned his fourth shutout for New England (6-9-5), which is just 1-7-2 on the road.
Each goalie had to make a spectacular save to preserve the draw. Nielsen punched out Ryan Guy's header in the 15th minute, and Reis made a diving fingertip save to deflect Jacob Peterson's header in the 52nd.