The first-year Duck, who would an assist later on, has points in back-to-back games (1-2=3) and ranks fourth among team leaders in goals (eight) this season.
The Ducks very nearly took that two-goal lead back to the locker room, but penalty issues that have plagued the club throughout the season reappeared at an inopportune time and would wipe that edge out by the early stages of the third.
The longest tenured Oiler, Nugent-Hopkins, got the home side back within one in the final minute of the second, getting to a loose puck in the low slot that had bounced off several skates in front of Dostal.
Nugent-Hopkins, the first pick in the 2011 NHL Draft, has points in three straight games and seven of his last eight. With 36 points in 32 games this season, Nugent-Hopkins in on pace to average more than one point-per-game for the first time in his 12-year NHL career.
McDavid brought the Oilers back level early in the third on another power-play goal. With Anaheim shorthanded 5-on-3, McDavid darted hard to the backdoor, taking a cross-seam pass from Draisaitl and beating Dostal high to the short side.
With two points on the night, McDavid extended his scoring streak to 12 games, the fourth such run of his NHL career. Only two active NHLers have more 12-game point streaks, Patrick Kane (six) and Nathan MacKinnon (five).
The Edmonton captain has power-play goals in three straight games.
Surrendering a two-goal lead to find themselves tied in the third period for the second straight game, the Ducks would turn to a familiar face for the decisive goal, with Klingberg once again coming through in the clutch.
After a failed Oilers defensive zone clearing attempt, Klingberg activated from his right point position to retrieve a bouncing puck at the hashmarks of the right wing wall. The Swedish blueliner got rid of the puck quickly while under pressure from an Oilers backchecker, lifting a blocker-side shot that seemed to surprise Skinner, who could not fight through a friendly-fire screen to keep the puck out.