Cullen's snap shot in the third round slipped between Corey Crawford's legs, and Patrick Sharp then hit the crossbar for Chicago. The Blackhawks and San Jose were the only teams to start 6-0 this year. The Wild improved to 4-1 at home.
Goals by Andrew Shaw and Jonathan Toews early in the first period prompted the Wild to pull goalie Josh Harding for Niklas Backstrom.
Cal Clutterbuck also scored for the Wild, and Backstrom stopped all 28 shots he saw.
Crawford, off to a sharp start in his third season as Chicago's primary goalie, made 23 saves as the Blackhawks started a season-long six-game road trip. They've played five straight one-goal games.
CANUCKS 3, AVALANCHE 0
VANCOUVER, British Columbia (AP) — Roberto Luongo made 24 saves for his first win of the season, helping the Canucks to the victory.
Luongo, who has been on the trading block since Cory Schneider replaced him as Vancouver's No. 1 goaltender, was rarely tested but still made some big saves in his 61st career shutout.
With the Canucks leading 2-0 in the third, Luongo stopped Matt Duchene on a short-handed breakaway that prompted calls of "Luuu, Luuu" from Canucks fans. He blocked a John Mitchell shot from the slot later in the period.
Jason Garrison and Max Lapierre each scored for the first time this season, and Zack Kassian picked up his fifth goal in seven games.
OILERS 2, COYOTES 1, OT
GLENDALE, Ariz. (AP) — Nail Yakupov scored a power-play goal at 3:52 of overtime and Edmonton fought back after giving up a goal late in regulation.
The Oilers appeared to be on their way to helping Devan Dubnyk to his fifth career shutout, but put their goalie in a bind when Sam Gagner was called for a penalty and the Coyotes pulled goalie Chad Johnson.
Nick Johnson took advantage, whipping a shot past Dubnyk's glove side with 19 seconds left in regulation after teammate Radim Vrbata failed on a backhander.
Yakupov ended it in overtime, punching in a rebound after a shot by Ryan Whitney caromed off teammate Taylor Hall.
Dubnyk stopped 27 shots and Lennart Petrell scored his first goal since Feb. 27, helping the Oilers end a five-game losing streak to Phoenix.
Chad Johnson had 19 saves after notching his first NHL shutout two days earlier.
SENATORS 5, CANADIENS 1
OTTAWA (AP) — Daniel Alfredsson scored his first goal of the season to lead Ottawa to the victory.
Jim O'Brien, Mika Zibanejad, Chris Phillips and Chris Neil also scored for the Senators, and Craig Anderson had 31 saves in his 300th career game.
Tomas Plekanec scored for Montreal, which had won four straight. Peter Budaj made 22 stops in his season debut.
Down 4-1 in the third, the Canadiens made a desperate push to get back in the game, but Anderson made numerous point-blank saves, including two on Brandon Prust.
Neil made it 5-1 with a wraparound goal with just over five minutes left.