Evan Bouchard and Ryan Nugent-Hopkins, who became Edmonton's all-time leader in games played (1,038) on Tuesday, each had a goal and an assist for the Oilers (11-2-3). Kasperi Kapanen had two assists and Tristan Jarry made 31 saves for Edmonton, which lost for the first time in eight games on the road this season (7-0-1), but does have points in its past five games (3-0-2).
"I don't know what was going on (in the second period)," Edmonton coach Mike Babcock said. "They were way better than us. They were way faster. We just kept turning it over. We feel fortunate to get a point here tonight. They were better than us."
Connor McDavid had one assist to extend his season-opening point/assist streak to 16 games. The Oilers captain leads the NHL with 31 assists.
Arseny Gritsyuk scored in the top of the fourth round of the shootout and Hellebuyck stopped Kapanen to secure the victory. Jesper Bratt also scored in the shootout for the Devils, and McDavid for the Oilers.
"I do have a little bit of a plan (in shootouts)," Bratt said. "But you've taken so many shootout shots throughout your career, you kind of just know what your strengths are and goalies’ weakness. You try to expose that, and I think me and 'Gritz' did a good job there."
Bouchard gave the Oilers a 1-0 lead at 8:29 of the first period on a slap shot from the top of the left face-off circle.
Brown tied the game 1-1 with a power-play goal at the left post at 7:42 of the second period, chipping in the loose puck on the rebound of his netfront redirect of a Hughes shot.
"It was nice to get a couple bounces," Brown said. "I thought we did a good job of kind of taking what they gave us. They're pressuring so we kind of simplified and got the puck to the net."