Kuznetsov skated the puck along the top of the zone, faked a pass to Ovechkin and then charged the net from the left side. He went untouched to below the left circle and beat Al Montoya stick side.
The Capitals have won two in a row and seven of their past eight.
Jussi Jokinen opened the scoring for Florida early in the second with assists from Dave Bolland and Alex Petrovic. Washington's Jay Beagle tied it 2:23 into the third period.
Washington goaltender Philipp Grubauer made 26 saves. Montoya had 25 for Florida.
The Capitals went to the power play after defenseman Erik Gudbranson held Ovechkin 42 seconds into the second period. As the power play was ending, defenseman Petrovic blocked a hard slap shot from the point, and it was gathered by Bolland, who lofted a short pass to Jokinen.
Jokinen chipped the puck on the second bounce and popped it over Grubauer for his third goal to give Florida a 1-0 lead at 2:47.
"Bolland made a great play," Jokinen said. "I swung, didn't hit the puck, but the second time I got it. That was a big goal."
Jokinen moved to the top line in place of injured Jaromir Jagr, and he nearly added another with 6:40 left in the period when he fired a loose puck in the slot, but the slap shot rang off the crossbar.
Montoya stood strong the remainder of the period, making a sprawling save on a Brooks Laich's put-back near the crease.
Florida's Connor Brickley then went off for interference on Marcus Johansson, but Montoya stopped the ensuing Washington power play that featured plenty of zone time.
The Capitals tied it when Beagle tipped in a shot by Ovechkin that was deflected by a sliding Jokinen in the slot.
Florida coach Gerard Gallant challenged the tying goal, saying Williams interfered with Montoya while skating through the crease. The call on the ice was confirmed after a short review, giving Beagle his second goal.
Florida's Rocco Grimaldi, recalled from the AHL earlier in the day, nearly won it off Bolland's shot in regulation's closing seconds, but Grubauer stopped Grimaldi's rebound shot.
Grubauer gloved Florida's best chance late in the first period after Nick Bjugstad split defensemen Karl Alzner and Matt Niskanen then flipped a shot from the low slot.
The game was the first meeting this season between the two clubs. They were rivals in the Southeast Division for 14 years before the Eastern Conference split into the Atlantic and Metropolitan Divisions after the 2012-13 season.
NOTES: The Capitals feasted on the Atlantic Division last season, going 16-4-4 and have earned a point in 18 straight games against the division (15-0-3). . Washington scored four or more goals in five of their first nine games and rank fourth in goals per game (3.56). . Florida scratched top scorer Jagr (lower body) for the second straight game. ... The Panthers placed F Aleksander Barkov (broken hand) on IR and recalled F Grimaldi from the AHL's Portland Pirates. ... Florida won an NHL record 20-round shootout the last time they hosted Washington on Dec. 16, 2014. The Panthers became the first team to tally six goals in a shootout.