Zach Parise scored midway through the third period and Petr Vrana tallied with 1:52 to play for New Jersey (2-2), which had a two-game winning streak snapped.
Nylander, who is making a comeback from shoulder surgery in January that limited him to 40 games last season, made two lovely passes on the first two goals.
With the Capitals on a power play, Nylander took a pass from Nicklas Backstrom, skated to the left side of goaltender Kevin Weekes and then slid a pass across the crease to a wide-open Green.
The defenseman who led the NHL with 18 goals last season slammed the puck into an open net for his first goal at 3:09.
A little more than four minutes later, Nylander lifted a pass from the right circle that found Gordon all alone in front for an easy backhand goal.
Nylander now has two goals and four assists in three preseason games.
Ovechkin, who scored 65 goals last season, got his third goal in two preseason games on a 2-on-1 rush with David Steckel. Ovechkin carried the puck into the zone, sent a cross-ice pass to Steckel and then dunked the return pass with Weekes out of position.
After Johnson stopped all 18 shots he faced in the opening two periods, Parise scored in close after taking a pass from David Clarkson. Vrana deflected a shot by Sheldon Brookbank for the other goal.
Johnson made 13 saves in the scoreless first period, with his best being a snapping glove save on Fedor Fedorov, whose brother Sergei was given the night off by Washington coach Bruce Boudreau.
Notes: Capitals enforcer Donald Brashear got the better of Pierre-Luc Letourneau-Leblond in a long third-period fight. ... The game at the Prudential Center drew 8,536 fans.
