Matias Maccelli and Barrett Hayton each scored twice, Lawson Crouse had three assists and Karel Vejmelka made 24 saves for the Coyotes (27-35-13), who have lost five straight (0-3-2), including 4-3 in a shootout against the Colorado Avalanche on Sunday.
Nugent-Hopkins gave Edmonton a 5-4 lead at 12:05 of the third period on the power play after Arizona rallied with back-to-back goals from Maccelli at 3:52 and Hayton at 4:50 to tie it 4-4.
"They kind of hemmed us in on a few shifts [in the third] and we kind of we lost our momentum, but you weather the storm," said Oilers forward Zach Hyman, who scored his 32nd goal in the first period. "We got some big special teams goals, and that changes the game. We got a big two points, and we'll keep rolling."
Maccelli made it 1-0 at 3:50 of the first period, but Hyman scored six seconds into an Edmonton power play at 4:40 to tie it 1-1, redirecting McDavid's pass to the left post.
Maccelli had his first NHL multigoal game while defending against McDavid's line.
"He had two goals playing McDavid, and you should get an award just for that," Coyotes coach Andre Tourigny said. "He played really good defensively, and now he's learning to put more pucks on the net and he is successful."