Hayes added to that lead with 4:19 left in the middle frame, spinning and firing a shot from the bottom of the right circle that beat Rinne short side.
"We had a real good effort. Everybody did their job and played hard," said Maurice. "Each line looks different, they have different roles. They played hard. I'm happy for them."
That wrapped a second period that saw the Jets outshoot Nashville 19-9. Overall, Winnipeg held a 35-20 edge in shots over the final 40 minutes.
"We had four lines and six D all over them all night. That's a real weapon for us," said Wheeler, who had five shots on goal in 19:04 of ice time. "We have four capable lines that can just feed off one another. If we can play at that tempo, we're tough to play against."
In the third, Connor finished a 2-on-1 with Hayes using a quick deke in front of Rinne for his second of the night, then capped off the hat trick with nine seconds left in regulation - blasting home a one-timer off a pass from Patrik Laine.
"That whole play starts with my line mates. They were joking that they were looking for me on that last shift. Patrik made a great pass," said Connor.
"He's a very underrated passer. I don't think that gets enough recognition. It's been really fun playing with him."
The hat trick goal sent Bell MTS Place into a frenzy, the perfect end to a night that brought a playoff-like atmosphere that didn't go unnoticed.
"That was a little bit of a different buzz than we've had in the building all year," said Wheeler. "Everyone was fired up for this one. We fed off that. I thought it was our best game of the year."