Scott Wedgewood made 39 saves for the Coyotes (4-14-2), who won their previous two games and had a four-game point streak (3-0-1).
"That's the kind of team the Edmonton Oilers are," Arizona coach Andre Tourigny said. "You give them a chance to get going, and they will. They have talented players, world-class players."
Oilers coach Dave Tippett reunited Draisaitl, McDavid and Kassian on his top line, and they combined to score 11 points. Draisaitl's second goal, on a power play, made it 4-1 at 13:08 of the third period.
"I thought we'd become a little stale the last three or four games, so we tweaked some things and got rewarded," Tippett said.
Travis Boyd scored 35 seconds later for Arizona at 13:43 to make it 4-2, and Shayne Gostisbehere cut it to 4-3 at 15:06.
McDavid scored an empty-net goal with 28 seconds left for the 5-3 final.
''It would have been easy at 4-1 to close the door,'' Tourigny said. ''Not once this year have I had to address the effort of our guys. Again tonight they fought hard. They battled.''
Clayton Keller gave the Coyotes a 1-0 lead at 3:45 of the first period on a 2-on-1 with Phil Kessel. Keller had a goal and two assists.
McDavid tied it 1-1 at 14:58 with the first of Edmonton's two power-play goals. The Oilers have the NHL's best power play (23-for-59, 38.98 percent).
"We had a good start to the game, but then the second period and the first part of the third, we were kind of waiting for something to happen," Coyotes defenseman Anton Stralman said. "They slowly turned it around and we were on our heels a little too much."