A city policeman picked the pair up at the airport and escorted them to both University Hospital and St. Paul's Hospital, allowing Gulutzan and McLellan to visit with victims of the crash - players, team staff on the bus - as well as with family members.
"We wanted to show them we were thinking of them,'' said Gulutzan. "That in some small way that we were supporting them. And maybe just kind of, hopefully, gave them a piece of relief for a few minutes.
"We thought we'd let the game speak. That's our common denominator. The game. Some of the guys wanted to talk a little hockey. About T.J. Brodie or Johnny (Gaudreau) or Connor McDavid.
"Quite a few Calgary and Edmonton fans among those there.
"So a lot of hockey talk.
"And hugs. A lot of hugs."
McLellan had reached out to Gulutzan on Saturday morning, proposing the two men make the trip. With a day off between season's end and exit meetings with players, the Flames' boss didn't blink in accepting.
Since news of the tragedy, the depth of support - emotional, spiritual, financial - has been nothing short of staggering.
A GoFundMe page set up to aid those affected has topped $4 million in a day. People from all walks of life, all corners of the world, have sent well-wishes and encouragement.
"Oh, I sensed they understand the outpouring of support from everywhere outside, and they're grateful for it, but it's obviously not their focus,'' Gulutzan replied.
"We had a few families say to us that sometimes it takes times like this, tough times, to see how much good there is in the world, in people.
"And how you just wish it could be there all the time."