Nilson scored the winning goal, his first of the season, and had an assist in Calgary's 2-1 victory over the Columbus Blue Jackets on Thursday night.
"It felt great to contribute," Nilson said. "I've had a pretty slow start offensively."
Steve Reinprecht also scored for the Flames, who won consecutive games for the first time this season to improve to 6-7-2.
David Vyborny scored the lone goal for Columbus, which lost star forward Rick Nash to another injury. Marc Denis kept the game close by stopping 29 shots. The Blue Jackets, 1-7 on the road, have lost three straight to drop to 4-10-0 overall.
Nash, the No. 1 selection in the 2002 draft, hurt his left knee when he was hit in the third period. He said he was day-to-day but expects to miss Friday night's game against Vancouver.
The 21-year-old Nash has already missed 11 games this season with a high right ankle sprain.
"I've already been frustrated all year," said Nash, who hobbled to the team bus after the game. "There's no point getting more frustrated. I don't know what to do anymore. It's part of the game. It's an injury. I've got to stay positive."
Vyborny scored his third goal of the season 59 seconds into the second period to give the Blue Jackets a 1-0 lead. With Calgary goalie Miikka Kiprusoff down on the ice, Vyborny wristed a shot over the fallen goalie's outstretched glove.
The Flames tied it at 3:09 of the third when Reinprecht kicked a rebound onto his stick and slid the puck past Denis, who was playing with a defenseman's stick after losing his own.
It was the first time a Calgary forward other than Iginla scored since Chris Simon had two goals in a 3-2 win over the Kings in Los Angeles on Oct. 23.
"We've lost a few games where it's been by one goal and nobody else but Iggy has scored," Reinprecht said. "Some of us, that's our role, to chip in and we haven't been able to do that, so tonight it was nice to contribute."
Nilson scored his first goal of the season at 10:36. Chuck Kobasew took the initial shot, which Denis batted out of the air toward Nilson, who was skating hard to the net. The puck bounced off both Nilson and Denis and across the goal line before the net came off its moorings.
After video review the goal stood, much to the delight of the sellout crowd of 19,289 at the Saddledome.
"That's the way our team is going to score a lot of our goals," Nilson said. "We're not a tic-tac-toe team. We need a lot of shots and a lot of rebounds."
After scoring a power-play goal in seven straight games, the Flames went 0-for-7 with the man advantage. Columbus was 0-for-3.
"It's disappointing to lose coming into the third period with a 1-0 lead, but they worked hard and they got a couple of breaks," Blue Jackets coach Gerrard Gallant said.
Notes: Iginla's four-game goal scoring streak and seven-game points streak ended. ... The Flames have won four straight against the Blue Jackets. ... Robyn Regehr returned after missing Calgary's first 14 games due to a knee injury he sustained in the preseason. ... The Flames still haven't scored more than three goals in a game this season.