It took three goals by the Oilers in the third period just to force the extra session and Nugent-Hopkins tallied on the power play 1:01 into the overtime. It was his second goal of the game.
Pittsburgh had won three in a row and leads the Metropolitan Division by 15 points, but could not take advantage of the team with the worst record in the Western Conference.
The Penguins held a 2-0 lead heading into the third period, but Edmonton tied the contest on goals Nugent-Hopkins and Taylor Hall during the first 10 minutes of the stanza.
Pittsburgh went back in front on a power-play goal by Kris Letang with 7:44 to go in regulation, after which Anton Belov again lifted the Oilers into a tie with the first score of his NHL career.
Belov, a defenseman, was playing in the 39th game of his rookie season.
Devan Dubnyk made 25 saves to get the victory. Jeff Zatkoff allowed the four goals on 31 shots.