Canadiens prevail in shootout
Kovalev put a backhand past Tomas Vokoun, who stopped Montreal's first two attempts by David Desharnais and Andrei Kostitsyn.
Carey Price stopped Florida's Nathan Horton, Michael Frolik and Ville Peltonen in turn in the shootout after making 36 saves in regulation and overtime.
"Hopefully he doesn't make all of them right now," Kovalev said. "He's ready to go and prove to a lot of people how good he is."
Anthony Stewart and Horton staked the Panthers to a 2-0 lead with goals early in the first and second, respectively.
Kostitsyn and Yannick Weber scored power-play goals later in the second to draw Montreal even at 2.
Vokoun, who entered with a 5.93 goals-against-average after allowing nine goals in his first two outings, stopped 33 shots overall.
"He was outstanding," Panthers head coach Peter Deboer said. "Without him tonight, obviously, we probably don't get a point, but he was fantastic."
Stewart scored his second goal in four preseason games early in the first period when he drove a slap shot from the top of the right faceoff circle over Price's glove to open the scoring 3:12 in.
Horton put Florida up by two with his first goal in three games 4:23 into the second. The Panthers center had a chance to extend the lead at 9:03 after he was hauled down on a breakaway, but was stopped by Price on the ensuing penalty shot.
"I tried to hit him to make him think I'm going there next time - how's that for an answer?" Horton said of his two failed attempts against the 21-year-old goalie. "Although, he's a pretty good goalie, I've got to give him credit."
Kostitsyn drew Montreal within 2-1 when he scored with the man advantage at 10:57, and Tomas Plekanec got his second straight assist on Weber's tying goal on another Canadiens power play at 14:22.
Price made a fine save 1:17 into overtime when he slid across to stop Peltonen's shot from the right edge of the crease.
"I just tried to get a good push over there," Price said.
Vokoun came up big in the final moments of the extra period when Montreal threatened after Panthers defenseman Noah Welch was penalized for holding.