Mikael Tellqvist made 30 saves for Phoenix, which has won four of its last five after struggling throughout the first half of the season.
The Capitals scored once during seven power plays. They've lost five straight and seven of eight.
The Coyotes have been looking for more offensive punch all season, especially on the power play. Phoenix entered the game ranked 29th in the NHL on the power play but scored twice in five chances.
Both goals came in the first period and helped the Coyotes take a 3-1 lead after one.
Nolan gave Phoenix an early 1-0 lead with a power-play goal 2:02 into the game, but Brian Pothier's power-play goal tied it for Washington with 6:17 left in the period. It was the defenceman's first as a Capital and ended a streak of 51 games without a goal.
Keith Ballard broke the tie when he took a Nolan pass and fired a wrist shot past Washington goalie Olie Kolzig for a 2-1 lead with 3:04 left. Shane Doan added the Coyotes' second power-play goal of the period with 14.1 seconds remaining.
Brian Sutherby cut the lead to 3-2 midway through the second period on a shot from the left circle for the Caps.
Notes: Donald Brashear of Washington served his one-game suspension for his role in Saturday's fight-filled loss to the New York Rangers. . . . Sutherby's goal ended a streak of 29 games without one. . . . Nolan's assist was the 400th of his NHL career. . . . Coyotes centre Yanic Perreault added two assists.