Coyotes coach Rick Tocchet said, "We just have to get a couple of our guys to understand that, in key moments, you have to play through the whistle."
Marchessault said the Golden Knights were rewarded for keeping the play going.
"You just kind of play through until there's a whistle, and obviously [there] wasn't one," Marchessault said. "I saw 'Tuchy' have the puck around the red-line area, and he tried to pass to me, but it hit something. I just kept going, and it didn't even cross my mind that it was going to be icing. Everybody stopped playing a little bit, but I just kept my head up and I saw Will alone, and he was able to bury it."
The goal was Karlsson's second this season and 18th game-winner in the NHL.
"I saw 'March' didn't give up on the play, we got the bounce, he got the puck, and I was kind of clear in front of the net," Karlsson said. "The name of the game was patience. We had a lot of chances and, sooner or later, they will go in."
Vegas outshot Arizona 19-11 through the second period and had two excellent opportunities to take the initial lead on the same shift in the second.
Marchessault had an opening inside the near post, but the puck came off his stick in the crease just before he could shoot. Seconds later, Reilly Smith's shot from the high slot deflected off the crossbar at 13:08.
Early in the third, Coyotes forward Phil Kessel was open in front, but Fleury covered in time as he tried to go five-hole. On the next shift, Fleury was screened and didn't see a Johan Larsson shot from the left face-off circle, but it deflected off the post.
Fleury, alternating starts with Robin Lehner, is 3-0-0 and has allowed three goals on 61 shots (.951 save percentage).
"The guys have been great in front, making my job a little easier, blocking a lot of shots and clearing in front of me," Fleury said. "We've scored some big goals, and this was a battle to the end."
NOTES: Vegas has trailed or been tied after the second period in five of its six games. … Golden Knights forward Mark Stone's five-game point streak ended. He had eight points (two goals, six assists) in the run. … Vegas was 0-for-2 on the power play and is 2-for-20 this season. … The Coyotes failed to score in the second period for the first time this season. They had seven goals in the second in their first five games.