Kuznetsov got a breakaway and beat goalie Connor Hellebuyck (40 saves) with a high shot in an overtime where Washington had all seven shots.
Ovechkin finished with two goals after not scoring a point in the past three games. However, he scored once in each of the first two periods to become the 20th player ever to reach the 600-goal milestone.
In addition, Ovechkin became the fourth NHL player to reach 600 goals in less than 1,000 games - this was the 990th game of his career.
Wayne Gretzky, Mario Lemieux and Brett Hull are the others.
Erik Haula, William Karlsson and Ryan Carpenter scored one goal each to lift Vegas past Philadelphia at the Wells Fargo Center.
Golden Knights goaltender Marc-Andre Fleury stopped 38 shots in earning his 400th career win, third among active players. It was Vegas' 45th victory this season, an ongoing record for an expansion franchise in the National Hockey League.
Claude Giroux and Wayne Simmonds scored for the Flyers and goaltender Petr Mrazek made 26 saves in the loss.
Four players scored a goal each and Jake Allen made 20 saves for just his fourth win in 21 games as St. Louis dumped Anaheim in a matchup of Western Conference playoff hopefuls in Anaheim.
Patrik Berglund gave the Blues valuable insurance with his ninth goal at 11:28 of the third period, taking a pass in the high slot from Kyle Brodziak and wiring a wrister by John Gibson. It was the second straight win for the Blues, who moved within a point of Colorado for the conference's last playoff spot, three days before they host the Avalanche.
Derek Grant pulled the Ducks within a marker at 6:15 with his ninth goal, deflecting a Chris Kelly shot, but Anaheim couldn't avoid its third straight loss. It stayed at 80 points, good for third in the Pacific Division, after going 7-1-1 in its previous nine games.
Goaltender Jonathan Quick stopped 35 shots for his fourth shutout of the season as hometown Los Angeles blanked Vancouver.
With the win, the Kings moved above the National Hockey League playoff bar. Their 81 points put two points behind San Jose for second place in the Pacific Division. L.A. also moved a point ahead of both Colorado and Anaheim in the Western Conference wild-card race.
Tyler Toffoli led the Kings with a goal and an assist, while Anze Kopitar, Tanner Pearson also tallied for the Kings as they posted their eighth win in 12 games.
Matt Duchene and Magnus Paajarvi scored two goals each as Ottawa snapped Florida's franchise-record eight-game home winning streak.
Florida's Aleksander Barkov nearly gave the Panthers their first lead of the game when he got a breakaway, shorthanded attempt with 5:51 left in the third period. But Barkov failed to fool Ottawa goalie Craig Anderson, a Broward County resident and a former Panther.
After Barkov came up empty, Duchene and Alexandre Burrows scored for Ottawa to snap a 3-3 tie.
Jimmy Vesey scored a hat trick, including the go-ahead goal midway through the third period, and Mats Zuccarello added two goals to lead New York to a win over visiting Carolina.
The Rangers snapped a three-game losing streak with the win, while the Hurricanes lost for the third time in four games.
Vesey scored the go-ahead goal with 7:45 left in the game, beating Scott Darling short-side for his 14th goal of the season. Vesey's goal came less than four minutes after a Victor Rask goal tied the score at three 8:23 into the period.