The Devils came up with a goal in each of the first two periods and hung on to hand Washington its seventh straight setback. The Capitals' eight road wins are the second fewest in the Eastern Conference.
Stephen Gionta scored on a slap shot 4:57 into the game and Adam Henrique delivered a power-play goal 1:45 deep in the second period.
Both those goals came against Michal Neuvirth, who finished with 28 saves.
Schneider's bid for a shutout ended when Jason Chimera scored on a deflection just past the midway point of the third period.