Corey Schneider made 38 saves for his third shutout of the season and to hand the Coyotes their season-high sixth straight loss in a row.
Scott Gomez opened the scoring the first period before Mike Cammalleri doubled the lead in the third. Matt Grzelcyk added a third in the first shot of overtime.
Elsewhere, the Anaheim Ducks rallied past the Detroit Red Wings for a 4-3 win on Monday night. They had looked out of the match before scoring three goals in an incredible four minute flurry in the third period to take the lead.
Anaheim, who are unbeaten on Monday night matches, had not won at home in the regular season since January 21. They host Ottawa on Wednesday while the Red Wings continue on their six-game trip on the road on Tuesday against the Kings.