Naslund, who missed several chances during regulation time, deked Washington goalie Olie Kolzig and scored on a backhand.
Morrison threaded a puck between Kolzig's legs minutes after Alex Ovechkin's attempt hit the inside post.
The Canucks won for the fourth time in five games to improve to 7-4-1, while Washington suffered its third shootout loss in seven games and slipped to 3-2-4.
Kolzig was brilliant, making 42 saves after an impressive 45-save effort Wednesday night in a victory over the Dallas Stars.
In the final eight minutes, he sprawled to beat Lukas Krajicek, stopped a Kevin Bieksa blast from trickling through, and saw Henrik Sedin graze the goalpost.
After being outshot 16-1 in the opening period, the Capitals got a lift from a power-play goal to earn a 2-2 tie entering the third period.
Zubris got his fourth goal in five games at 16:49 of the middle frame when Washington enjoyed a 5-on-3 advantage. He was alone at the side of the net when an Ovechkin shot deflected to him off a Vancouver defender, catching netminder Roberto Luongo out of position.
Ovechkin tied the game one minute 33 seconds later when he darted to the net to convert Brian Sutherby's backhand pass eight seconds after Vancouver's second penalty expired.
The Canucks scored twice in the first period but squandered several other chances or were foiled by Kolzig's solid goalkeeping as Vancouver outshot Washington 44-21 over 65 minutes.
Bulis opened scoring when Morrison found him in the slot with a pass from behind the net and his quick shot trickled behind besieged Kolzig.
Pyatt got his fourth goal in five games and sixth of the season when he re-directed Henrik Sedin's pass from the side boards on a Vancouver power play.
NOTES: It was the Canucks' first outing after a five-game road trip ... they play eight of their next 10 at GM Place ... Capitals defenceman Shaone Morrisonn, a Vancouver native making his first NHL appearance here, purchased 40 tickets for family and friends ... Vancouver debuted a new scoreboard by wearing their vintage blue uniforms.