Mike Green and Brooks Laich also scored for the Capitals, who scored three times on the power play and have won three straight games. Jose Theodore made 32 saves for Washington, which earned at least a point for the seventh time in its last eight games overall (6-1-1). Alex Ovechkin posted two assists in the win.
Jamie Langenbrunner and Brian Rolston scored for the Devils, who sought their first nine-game win streak since late November of the 2007-08 season but fell short and lost for the first time since January 11 at Anaheim.
Scott Clemmensen allowed four goals on 25 shots in the losing effort.
The Capitals struck early with a pair of power-play goals before the midway point of the opening period.
At the 4:17 mark of the first, the Devils were whistled for having too many men on the ice and the Capitals cashed in. Alexander Semin held control high along the left side near the half-wall and sent a pass across the slot for Green, who pinched in from the right point, accepted the pass inside the lower right circle and beat Clemmensen with a wrister at 5:58.
Soon after, Langenbrunner went to the penalty box for a hooking minor and the faceoff after the whistle was inside the left circle in the Washington offensive zone. The puck was drawn back to the point and Green passed to Ovechkin below the right circle. Ovechkin momentarily faked a shot before he sent a quick pass to Laich, who tapped the puck across the goal line from atop the crease at 8:12, only four seconds into the power play.
Washington moved ahead by three 2:16 into the middle session on Nylander's sixth goal of the season. Boyd Gordon's slap shot from inside the left circle was saved by Clemmensen, but the netminder failed to control the rebound and after several whacks at the puck from in close, Nylander pushed it into the back of the cage.
The Devils began to show signs of life midway through the second period. Several offensive rushes nearly produced a goal, the closest of which occurred with 12:30 remaining when Zach Parise hit the left post with a wrist shot. The Devils got on the board shortly after that Parise near-miss with a power-play tally.
New Jersey gained a 5-on-3 advantage thanks to penalties called on Green and David Steckel 41 seconds apart. The Devils worked the puck with ease around their offensive zone during the two-man advantage and Rolston held control in the high slot. Rolston then fired a slap shot that beat Theodore down low with help from a screen in front by Travis Zajac with 11:10 to play in the stanza.
Only 41 seconds into the third, the Devils cut their deficit to 3-2 courtesy of Langenbrunner's short-handed breakaway goal. David Clarkson's hooking minor inside the final minute of the second period carried over into the third, but a turnover by the visitors led to an outlet pass from Zajac to Langenbrunner, who skated in all alone from the right side and lit the lamp with a wrister.
However, Nylander's second tally of the game -- a wrist shot from inside the lower right circle while the Caps were on the power play -- with 9:01 remaining in regulation essentially iced the victory. Nylander held control inside the circle and looked for a cutting teammate, but with no open passing lanes, he finally decided to take a shot and it beat Clemmensen through the five-hole.
Eric Fehr's empty-net goal at 18:50 capped the scoring.