Draisaitl had the secondary assist on Corey Perry's first-period goal, and has 27 points (14 goals, 13 assists) during the streak.
Viktor Arvidsson and Connor McDavid scored for the Oilers (39-24-4), who are second in the Pacific Division, four points behind the Vegas Golden Knights and one ahead of the Los Angeles Kings. Ryan Nugent-Hopkins had three assists, and Stuart Skinner made 21 saves.
"[Skinner] was outstanding," Nugent-Hopkins said. "Their goalie on the other side, he's an elite goalie. (Skinner) stepped up and made some huge saves when we needed him to and stayed composed, but he kind of led the way.
Will Cuylle scored for the Rangers (33-29-6), who kept hold of the second wild card into the Stanley Cup Playoffs in the Eastern Conference, one point ahead of the Columbus Blue Jackets, and five behind the Ottawa Senators for the first wild card. Igor Shesterkin made 20 saves after recording 21 in a 4-0 shutout against the Blue Jackets on Saturday.
"I thought it was a tight hockey game, a good hockey game going into the third period," New York coach Peter Laviolette said. "They scored one. We pressured, we had lots of chances, lots of look, couldn't get the next one to fall."
Perry gave Edmonton a 1-0 lead with a power-play goal 43 seconds into the first period. He tipped a shot from Draisaitl that was stopped by Shesterkin, before converting on a rebound in front.
Cuylle tied it 1-1 at 5:00 of the second period when the puck was in the crease behind Skinner and he shot it in. Artemi Panarin, who had an assist on the goal, extended his point streak to nine games (six goals, seven assists).
"I thought our energy was good despite the back to back, but we need wins at this time of year, especially, so there's no moral victories but we just got to turn the page and get ready for the next one," Cuylle said.