Stuart Skinner made 23 saves in his fourth straight start for the Oilers (10-9-0), who are 3-6-0 in their past nine games.
"There were individual errors in our game tonight, and you can't do that and expect to outscore mistakes," Edmonton coach Jay Woodcroft said. "We clawed back. There was game and fight in our team, and we made it 3-2 at the beginning of the third period with a chance to tie it. [Vanecek] made a really good save and, in the end, self-inflicted, individual mistakes cost us."
Bratt gave the Devils a 1-0 lead with a power-play goal at 2:25 of the first period on a one-timer from the slot.
"A lot of teams are looking at us as a very offensive, skilled team, but I think the thing that has helped us win games has been our depth, that we have four lines, three defense pairs that make a big impact and our goaltending," Bratt said.
Leon Draisaitl tied it 1-1 with a power-play goal at 13:02 on a quick shot from the bottom of the right face-off circle.
Mercer gave New Jersey a 2-1 lead at 5:15 of the second period on a turnover, and Severson extended it to 3-1 with a wrist shot from the high slot at 8:45.
"We don't get scared, we don't get back on our heels [when the game is close]," Devils coach Lindy Ruff said.