Connor McDavid had a goal and two assists, and Stuart Skinner made 31 saves for the Oilers (36-23-8), who had won two straight.
Edmonton holds the first wild card into the Stanley Cup Playoffs from the Western Conference, three points ahead of the Winnipeg Jets.
"The last eight minutes of that period, not our finest hour," Oiler coach Jay Woodcroft said. "Certainly situations within our control. We thought we got away from playing simple. We tried to pass through people and they're good team, they had good sticks and I just saw a lot of self-inflicted wounds during that little time frame there."
Marner cut it to 3-2 at 12:56 when he intercepted a cross-slot pass from Ryan McLeod and deked Skinner at the top of the crease.
"I just tried to put pressure, realized it was a forward and tried to make him feel uncomfortable and read the play, and lucky enough I was able to do so," Marner said.
Nylander tied it 3-3 at 14:49 when he took a pass from Marner, who stole the puck from Vincent Desharnais, and shot from just above the right hash marks. He has 34 goals this season, tying his NHL career high.
"We just kept getting turnovers and Mitch made some nice plays to get the puck and take the puck from them and score some big goals," Nylander said. "Just the way he reads the play on both of those, he was trying to make the guy make the play, and he read it so perfectly."
"With [his goal] and the play he passed it to me, he just took everything and took over the game for us."