WATCH: All Oilers vs. Bruins highlights
Ryan Nugent-Hopkins also scored, and Connor McDavid had two assists for the Oilers (20-13-7), who defeated the Bruins for the fourth straight time but first in regulation in 17 games since a 6-1 win Oct. 17, 2000.
The Oilers are 1-1-0 on their four-game road trip after a 3-1 loss to the Columbus Blue Jackets on Tuesday.
Colin Miller, Patrice Bergeron and David Krejci scored, and Tuukka Rask made 21 saves for the Bruins (20-17-4), who have lost two straight games after winning two in a row.
It was Boston's first game since Hockey Hall of Fame member Milt Schmidt died Wednesday, and the Bruins had a pregame ceremony to honor their former captain, coach and general manager.
"For sure a tough game to lose, especially on a night like this," Bruins defenseman Zdeno Chara said. "It was a night where it was dedicated to Milt and what he's done, and I felt we let him and obviously his family, including the fans, down. It's a tough way to lose. I thought we were obviously playing a tight game, and then again we lost it by mistakes made. It happened in the third and they got a two-goal lead, and we made it one goal but again fell short."