The Minnesotans thought they had whittled their deficit in half just past the midway mark of the second period, via Zach Parise.
In the build-up, Elliott produced a sharp close-in save, using his right toe to prod a Parise try away. The plucky Parise eventually did ram the puck past Elliott.
Incidental contact with the Flames goaltender, however, had been ruled on the ice and the strike was chalked off.
Undeterred, the Wild continued to press forward and were rewarded only a minute and a half later.
The goal began with Calgary defenceman Dennis Wideman's shot from the right point being blocked by an onrushing Jason Zucker.
Compounding the trouble, Wideman then stumbled, allowing Mikael Granlund and Zucker, hobbling but still mighty game to re-join the fray, to storm out 2-on-1.
Granlund cooly waited the lone surviving defenceman, TJ Brodie, down, then slid a backhand pass across to an unattended Zucker to convert.
Zucker's goal came after the locals had parlayed a strong opening nine minutes into a 2-0 lead.
First came Alex Chiasson's first goal in 11 starts, a timely deflection as he cruised in front, Sam Bennett with the arrangement.
Then, the predatory Monahan, coming late to arrive en scene as Johnny Gaudreau's nimble deflection was spit back by Dubnyk, cashed his 17th of the season at 8:09.
The Flames now head out east for three - to New Jersey, New York and Pittsburgh - before beginning a rare four-day break.
"We've got another three tough games coming up,'' reminded Elliott. "Three tough buildings.
"Putting away these two points is really what we wanted to do heading out."
They'd no doubt take a carbon-copy, a Xeroxed replica, of Wednesday's performance in all three of those tests.
"I think,'' offered Gulutzan, "that we're capable of lots of things if we stick with it and we believe in ourselves.
"I think what's growing in that locker room is the belief that if we stick to the game plan, play a certain way, we have enough skill to get us points every night.
"We've should grow from this game and now we've got to do it on the road against some other good teams."