“You don’t want to give up five goals, ever,” Draisaitl said. “That means you have to scramble offensively to win a game. We don’t want to be a team like that. Obviously the two points are big, we needed that, but there are lots of things we can do better defensively.”
Zack Kassian added two goals, and Connor McDavid and Evan Bouchard also scored for the Oilers (3-0-0).
“They can’t all be masterpieces,” Oilers head coach Dave Tippett said. “They can’t all be games where the coach walks out and says ‘That was great.’ It was good, we found a way to get two points.”
Kevin Shattenkirk and Sam Steel had two-goal games, and Nicolas Deslauriers also scored for the Ducks (2-2-0).
“I will say this, I’m proud of that group, back-to-back game playing against an elite team and the way we battled and stayed in it and kept coming back, never quit,” Ducks head coach Dallas Eakins said. “That’s a big step forward for us even though we didn’t get the points,”
Edmonton’s Mike Smith stopped 11 of 15 shots before leaving midway through the second period with an apparent injury. He was replaced by Mikko Koskinen, who had 20 saves in the win.
Anthony Stolarz stopped 31 of 36 shots for the Ducks, who were coming off a 3-2 overtime win against Calgary on Monday.
Anaheim grabbed a 1-0 lead five minutes into the first as Shattenkirk crept in and took a feed from Trevor Zegras, beating beat Smith up high.
Edmonton tied it four minutes later as Ryan Nugent-Hopkins sent a quick pass to Kassian at the side of the net and he directed it home before Stolarz was able to get back across.
The teams traded goals just 15 seconds apart with five minutes remaining in the opening period as Draisaitl sent McDavid in on a breakaway and he scored his fourth of the season. The Ducks got that back when Steel scored off a rebound.
Edmonton made it 3-2 on a two-man advantage with 30 seconds left in the period, as McDavid set up Draisaitl for his first of the season and the 200th goal of his NHL career.
Anaheim drew even nine minutes into the middle period when Ryan Getzlaf made a nice long pass to Deslauriers for the goal.
The Ducks then took the lead just over a minute later as Steel beat Smith for his second goal in his first game of the season.
Smith appeared to be injured shortly thereafter. He left for the dressing room and was replaced in net by Koskinen.
Edmonton tied the game just over five minutes into the third period when Kassian tipped home his second of the game on the power play.
The Oilers regained the lead midway through the third on a fluke goal as Bouchard swatted at the puck in the corner and it somehow went off of Stolarz’s pad and into the net.
“I honestly still don’t know how it went in, but I will take it,” Bouchard said.
Edmonton got a key goal with a minute left when Draisaitl scored into an empty net. Shattenkirk scored his second of the night with 19 seconds left to pull Anaheim back to within one, but the Ducks couldn’t complete the late comeback.
NOTES: Anaheim was without forwards Mason McTavish (lower body) and Max Jones (upper body), both injured in Monday’s game in Calgary.
Ducks: Game three of a four-game trip at Winnipeg on Thursday.
Oilers: At Arizona on Thursday.