The second came later in the game, when Connor snapped home a one-timer off a pass from Cale Makar with 2:08 left in regulation. This time, Connor wasn't so lucky, as the play was offside on the entry - as the review showed.
"Probably had more (reviews) in that game than there was in the season," Connor laughed. "We can joke and laugh about it, but at the bottom everybody wants to win, everybody is pretty competitive. I'm sure they were looking at it as soon as it happened."
There was no rest for Connor though, and it had nothing to do with preparing for the final.
He was one of many players who spent the time between games taking in Machine Gun Kelly's performance at T-Mobile Arena, as the platinum-selling recording artist descended from a small stage hoisted high above the ice surface.
"It was cool. I'm a fan of his music," said Connor, who posted his view on his Instagram story. "I thought it was great. It was cool to see him close up."
When the set was all cleared, Connor and his Central teammates took to the ice against the Metropolitan - who had disposed of the Pacific Division with a 6-4 score.
The teams traded goals in the first 1:38, with Arizona's Clayton Keller matching Washington's Evgeny Kuznetsov's tally.
But in a span of 1:17, the Metropolitan opened a 3-1 lead with goals by captain Claude Giroux - who finished as the All-Star MVP - and the NHL's leading goal scorer, Chris Kreider.
Down 3-1, the Central pulled within one on a goal from Nazem Kadri, a play set up by Connor, before Jack Hughes ended the first period with his third goal of the day to make it 4-2.
Once again, the Central got within one as captain Joe Pavelski scored his second of the day 1:19 into the second. Giroux answered quickly, though, rounding out the scoring in a 5-3 final.
Even if Connor and the Central didn't win the grand prize, he's still going home with a little something extra in his suitcase.
"There are a bunch of sticks and jerseys going around," said Connor. "I think we're getting two jerseys signed by everybody. That will be cool, something you can always look back on and remember experiences like that."