The center left Game 2 on Wednesday with an upper-body injury he sustained from a hit by Vegas defenseman Brayden McNabb with 5:18 remaining in the first period.
"I woke up, felt a little better again," Kuznetsov said. "I felt like I can help the team, and it ended up working pretty well for us."
RELATED: [Complete Golden Knights vs. Capitals series coverage]
Washington leads the best-of-7 series 2-1 with Game 4 here Monday (8 p.m. ET; NBC, CBC, SN, TVAS).
Kuznetsov was said to be a game-time decision after he participated in the morning skate and took rushes in his regular spot on the top line between Alex Ovechkin and Tom Wilson.
Kuznetsov scored 12:50 into the second period to give Washington a 2-1 lead.
"I think the shot, it's not my strong side," Kuznetsov said. "But that situation, we have a 2-on-1, I look for [Jay Beagle], and when you have a chance to feed those guys who play on the [penalty kill] a lot, who block a lot of shots, you want to make that pass for him. But he wasn't open that time and I had to shoot."