Kris Russell scored in regulation for the Oilers, who posted their second consecutive win.
Ryan Kesler tallied for the Ducks, who saw their three-game winning streak end.
Edmonton goaltender Cam Talbot and Anaheim counterpart John Gibson were both credited with 33 saves, and they each faced 34 shots.
The Oilers (18-20-3) outshot the Ducks 13-2 in the first period but could not beat Gibson, who returned between the pipes after getting a night off Tuesday when Anaheim won in Vancouver.
Russell opened the scoring on a power play at 11:58 of the second frame. He converted a pass from Connor McDavid during a three-on-two rush following a quick breakout from the Edmonton zone. With the assist, McDavid ended his pointless drought at three games.
Kesler created a 1-1 tie only 18 seconds into the third period on a double-deflection. He knocked in the puck after teammate Jakob Silfverberg also got his stick on defenseman Cam Fowler's shot. The goal was the first of the season for Kesler, who only resumed playing recently after recuperating from offseason hip injury.
Gibson withstood some severe pressure from the Oilers late in the third period to force overtime.
The Oilers got a power play early in overtime after the Ducks' Antoine Vermette was penalized for high-sticking McDavid late in the third period, but Gibson remained stellar again. Edmonton received another power play with 22 seconds left in the extra session as Fowler was sent off for slashing Darnell Nurse.
Before Nugent-Hopkins netted the winner, Anaheim's Rickard Rakell and Edmonton's Michael Cammalleri traded goals in the shootout. However, the shootout tally did not prevent Rakell's goals streak from ending at six games.
The Oilers played without winger Patrick Maroon, who served the first of a two-game suspension for a high hit on Los Angeles Kings defenseman Drew Doughty. Winger Corey Perry missed his 11th consecutive game with a knee injury for the Ducks (19-14-9).
During the game, the Oilers acquired goaltender Al Montoya from the Montreal Canadiens in return for a conditional 2018 fourth-round draft choice.
--Field Level Media
Anaheim | Edmonton | |
Ryan Kesler 1 | Points | Kris Russell 1 |
Ryan Kesler 1 | Goals | Kris Russell 1 |
Cam Fowler 1 | Assists | Milan Lucic 1 |
Ryan Kesler 1 | Power Play Goals | N/A |
N/A | Short Handed Goals | N/A |
John Gibson .971 | Save Percentage | Cam Talbot .971 |
John Gibson 33 | Saves | Cam Talbot 33 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Anaheim | 34 | 1 | 1-2 | 5-5 | 10 | 27 |
Edmonton | 34 | 2 | 0-5 | 1-2 | 4 | 34 |