Still, sweeping a set at the Chicago Blackhawks and St. Louis Blues on consecutive nights after starting the season 1-4-1 is reason to raise an eyebrow.
And a hope, or two.
"It was much needed on lots of fronts," Gulutzan said.
"I thought that our power play needed it.
"I thought that our team mentality above all needed it.
"I thought our goalie needed it. We gave him, finally, some run support and we gave him some help. We didn't turn over 27 pucks.
"All that other stuff we talk about here … we heard, 'They can't defend' and, 'They can't do this,' all that is by-products of turning pucks over and not giving yourself a chance to do that. We cleaned that area up and you see the rest of the game tighten up.
"We've got to continue to do that."
The power play, which had gone drastically cold after scoring in the season opener, connected twice in Chicago, and again in St. Louis.
Goaltender Brian Elliott, who surrendered 14 goals and hadn't won in his first three tries with the Flames, stopped 54 of 57 shots to scoop up back-to-back victories against the Blackhawks and Blues.
And the Flames, in general, seemed to finally latch onto Gulutzan's system of puck management in a big way.
All in time to host the Ottawa Senators at Scotiabank Saddledome on Friday.
"We got some results," Flames captain Mark Giordano said. "But in saying that it's only two games. We're still not in the spot we want to be as a team. We want to get better every day. We've got a lot of work to do, especially at home. We've got to come out with a good start tomorrow and play that same way.
"One thing about that trip, though, is we were a lot smarter with the puck at both bluelines and more direct. We got some results because of it.
"But we've got to still look at the big picture. We won two games in a sense, but we can't all of a sudden start feeling too confident. We've got to grind it out and play the same way and go from there."
Two wins, suggested the captain, are far from enough to rest on.
The coach knows it.
So too do the players.
"There are 74 games left," centre Matt Stajan said. "You can't get complacent in this business. That's when teams get themselves in trouble. We can be happy with the two but we can't feel like we've accomplished anything.
"That's something we're trying to get rid of. We've won a few and people let off the gas and think it's just going to happen. You've got to work even harder to keep it going. That's the attitude we need.
"It's so cliché and such a hockey player answer, but you've got to put your work boots on and come and do your job tomorrow. As a group, we've been guilty in the past of maybe getting too complacent when things start going well. That's the challenge here. We've got to work even harder when things are going well to keep it going. That's the focus.
"Everyone is going to go home tonight and go to bed knowing that."
Because the standings still show a team that sits 3-4-1 through the first eight games of the season.
"We're below .500," Gulutzan said. "We need to get on a roll. Two games isn't anything. What it is, really, truthfully, is it's a building block. It's something to step on. By no means have we got to the top. By no means have we identified ourselves as this type of team.
"But it's a step.
"We've got to keep building."