Cullen had two goals and an assist to lift the Wild to a 3-1 victory over the Edmonton Oilers on Thursday night.
"It was a step forward for us," Cullen said of the Wild, who are 2-4-1 away from home. "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 in the first game between the Northwest Division rivals in 420 days, dating 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," Wild forward Zach Parise said. "It is a good sign for us."
"We had put ourselves in a position to win and then gave up on the game that had brought us to that point," Oilers coach Ralph Krueger said. "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."
"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."
The play could also lead to supplemental discipline for Hall once the NHL reviews it.
Hall said the hit was purely accidental.
"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.
"I don't think it was a dirty play. I don't think I led with my knee."
Clutterbuck stayed on the ice, writhing in pain, before he was helped to the dressing room.
Minnesota took a 2-1 lead just over two minutes into the third period 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 midway through the period on a breakaway, but Sam Gagner sent a shot wide.
Cullen then gave his team a two-goal cushion with 6 minutes left when he chose to shoot on a 2-on-1 break and sent a high drive past Dubnyk.
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 with Gagner, but Backstrom came across to make the save.
Minnesota came close midway through the second with a flurry in front that included a huge save from Dubnyk in tight on a rebound from Dany Heatley, and another drive off the post.
Edmonton broke the scoreless deadlock 12:26 into the second when Smyth picked up a rebound behind the net and quickly looped around to put the puck in from the other side before Backstrom could get across.
It was the second goal of the season for Smyth, who celebrated his 37th birthday on Thursday.
The Wild tied it with five minutes to play in the period as Cullen outmuscled Mark Fistric to the puck and then beat Dubnyk with a backhanded shot through the legs.
It was the first of four games this season between the teams. Last season, the Wild won four of six after a six-game sweep in 2010-11. The Wild entered with a 27-8-2 record against the Oilers over the last six seasons. ... Oilers D Theo Peckham played in his first game of the season. Veteran D Ryan Whitney was a healthy scratch for the fourth time this year. ... Backstrom played after recovering from a bout with the flu. He improved to 23-3-1 against Edmonton. ... 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.