Deslauriers completed the hat trick at 11:49 of the first period to break the previous record set by Teemu Selanne, who scored three goals in the first 12:58 against the San Jose Sharks on Nov. 10, 1997.
It was the first hat trick in the NHL for Deslauriers, who entered the game with four goals in 57 games this season.
"I don't think even when I was younger I scored a hat trick, so it's something special," Deslauriers said. "I have to give credit to my line (David Backes and Carter Rowney). We've been working hard."
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Rickard Rakell had a goal and an assist, Backes and Rowney each had two assists, and Ryan Miller made 40 saves for the Ducks (29-32-9), who are 3-0-1 in their past four games and 5-2-2 in their past nine.
"Coming off the last game (5-4 overtime loss to the Minnesota Wild on Sunday), I felt like we kind of handed back at least a point, so I wanted to bounce back and continue to set the tone," Miller said. "I know where we're at (in the standings), but we have to be the kind of team moving forward that bounces back."