Hendricks deked around Penguins goaltender Jeff Zatkoff to start the shootout, and then Eberle put a quick shot between Zatkoff's legs. Oilers goaltender Anders Nilsson stopped David Perron and Sidney Crosby.
After Edmonton led 2-0, Pittsburgh's Evgeni Malkin scored his 10th and 11th goals early in the second period. The Penguins dropped their second straight and have lost three of four.
Edmonton also won in Pittsburgh for the first time since Jan. 10, 2006 and has won here just twice in 22 1/2 years. Edmonton lost eight of its previous 10 against the Penguins.