Draisaitl scored from the right face-off circle off a cross-ice pass from Connor McDavid.
"Every point right now is huge for us," said Draisaitl, who had two assists and extended his point streak to 14 games, the longest in the NHL. "We know the position we are in and we are trying to climb back into it. It was a huge win for us."
WATCH: [All Rangers vs. Oilers highlights]
McDavid and Matt Benning scored in the first period for Edmonton (31-31-7), which has won five of its past six games and trails the Minnesota Wild by five points for the second wild card into the Stanley Cup Playoffs from the Western Conference. Mikko Koskinen made 28 saves.
Brendan Lemieux had a goal and an assist, Brett Howden scored, and Alexandar Georgiev made 30 saves for the Rangers (28-28-13), who are 1-2-5 in their past eight games and trail the Columbus Blue Jackets by 10 points for the second wild card from the Eastern Conference.
"To get down 2-0 and play as poorly as we did in the first period, and come back to play with a lot more pace and lot more passion is certainly a great sign," New York coach David Quinn said. "Certainly, you'd like to do that for 60 minutes instead of 40, but give them credit, I though they played hard and they were dialed in from the start. I guess we had to adjust our pace if we were going to have a chance tonight."
McDavid scored on the power play 6:08 into the game, taking a pass from Alex Chiasson and shooting from the right face-off circle to give the Oilers a 1-0 lead.