The Minnesota forward had two goals and an assist on Thursday as the Wild defeated the Edmonton Oilers 3-1 to earn their first 60-minute win away from home this season.
"It was a step forward for us tonight," said Cullen, whose team improved to 2-4-1 on the highway. "It's a big deal for us to get a road win and it was good to see us respond to a bit of adversity and come back with a fight. I thought we did a good job. As a team we have to establish that. That when you are down one that you are going to be OK and make that push."
Devin Setoguchi also scored for Minnesota (8-6-2), which has won two straight. Niklas Backstrom made 25 saves to get the win for the Wild in the first game between the Northwest Division rivals in 420 days, dating back to December 2011.
"One of our problems this year has been responding when the other team gets a lead, but tonight we got it right back," said Wild forward Zach Parise. "It is a good sign for us."
Ryan Smyth scored for the Oilers (6-7-3), who have lost three of the first four contests of a five-game homestand in advance of a nine-game road trip. Devan Dubnyk stopped 25 shots in taking the loss.
"We had put ourselves in a position to win and then gave up on the game that had brought us to that point," said Oilers head coach Ralph Krueger. "That is definitely what is frustrating right now.
"The last 25 minutes, we need to be extremely angry and out of this anger find some solutions."
There was an ugly incident with 2:33 to play in the game when Edmonton's Taylor Hall hit Minnesota's Cal Clutterbuck knee-on-knee at centre ice. Hall was assessed a five-minute major and a game misconduct on a play certain to be reviewed by the league. Clutterbuck stayed on the ice writhing in pain and had to be helped to the Wild's locker-room.
"You hate to see those hits," Cullen said. "It was a fast play. I think it was deserving of the penalty. I'd be surprised if there wasn't a suspension of some kind. Cal is a very important part of our team and has been playing very well for us lately. You hate to see a teammate on the ice. It looked like it could be pretty bad."
For his part, Hall said it was purely an accident.
"I really didn't feel like it was knee-on-knee at all," he said. "I thought I got him with the hip or torso area. It was a weird play.
"It sucks to see him down, but I don't think it was a dirty play. I don't think I led with my knee."
Tied 1-1 after 40 minutes, Minnesota took the lead just over two minutes into the third when Cullen sent a pass in front to a streaking Setoguchi, who beat Dubnyk with a quick shot.
Edmonton had a chance to tie it up midway through the period but Sam Gagner sent his shot wide on a breakaway.
Cullen then gave his team a two-goal cushion with six minutes left to play by electing to shoot on a 2-on-1 and wiring a shot high past Dubnyk.
There was no scoring and few chances in a defensively-minded first period, the best belonging to Minnesota's Dany Heatley, who had Dubnyk beat on a quick shot but hit the post in the final minute.
The Oilers' best chance in the first half of the game came six minutes into the second when Nail Yakupov fed Gagner on a 2-on-1, but Backstrom came across to make the save.
Minnesota came close midway through the second period with a flurry in front that included a huge save from Dubnyk in tight on a rebound from Heatley and another post.
Edmonton finally broke the deadlock at 12:26 of the second when Smyth picked up a rebound behind the net and quickly looped around to put the puck in the other side before Backstrom could get across. It was the second goal of the season for Smyth, who was celebrating his 37th birthday.
The Wild quickly tied the game up with five minutes to play in the period as Cullen outmuscled Mark Fistric to the puck and then beat Dubnyk with a backhand shot through the legs.
Both teams return to the ice on Saturday. The Oilers conclude their homestand with a game against Phoenix, while the Wild are in Calgary to face the Flames.
Notes: It was the first of four games this season between the two teams. Last season, the Wild won four of six games after a six-game sweep in 2010-11. The Wild entered the contest with a 27-8-2 record against the Oilers over the last six seasons. ... Oilers defenceman Theo Peckham played in his first game of the season. Veteran defenceman Ryan Whitney was a healthy scratch for the fourth time this year. ... Backstrom played after suffering from a bout with the flu. He came into the game with a 22-3-1 lifetime record against Edmonton. ... Fellow Wild goalie Josh Harding (multiple sclerosis symptoms) was placed on injured reserve last week, while defenceman Tyler Cuma (foot) is still reportedly weeks away. ... Oilers forward Ryan Jones (eye) had been cleared for contact and could be back in the lineup on Saturday. Forwards Anton Lander (foot) and Shawn Horcoff (hand) are week-to-week.