J.T. Miller and Horvat scored in the third period to tie the game, and Thatcher Demko made 27 saves for the Canucks (32-28-10), who have lost three in a row.
"It's frustrating. We need every point we can get at this point," said Horvat, who was also stopped by Lehner on a shorthanded breakaway late in the first period. "I tried shooting quick on my break in the first period, and I wanted to change it up [in overtime], and he made another great save. If I score that game is over."
Vegas took a 1-0 lead at 6:51 of the first period after Stephenson won an offensive-zone face-off to Jack Eichel, who passed across to defenseman Alex Pietrangelo for a shot over Demko's shoulder from below the left face-off dot.
Marchessault made it 2-0 at 12:31, using defenseman Travis Dermott as a screen to shoot over Demko's glove from the hash marks on a solo rush from center ice.
"I don't know why we don't start on time," Canucks coach Bruce Boudreau said. "They had us at 10-1 in shots. I think teams know this and come out flying and we should be able to know that, hey, we've got to hold off and play hard for the first period."