Kucherov, the NHL leader with 108 points (31 goals, 77 assists), tied Vincent Lecavalier (56 goals, 52 assists in 2006-07).
"It's OK," Kucherov said of the record. "I just try to work on my game every day and see what happens, but it's good. I like it."
WATCH: [All Jets vs. Lightning highlights]
The Lightning (51-12-4), who are 12-1-0 in their past 13 games and 14-1-2 in their past 17, lead the NHL with 106 points and lead the Boston Bruins by 17 points for first in the Atlantic Division. Andrei Vasilevskiy made 30 saves for his 10th consecutive win.
"They are a heavy team, have some big guys," Kucherov said. "We just wanted to come out and play hard. They are a top team out there, and we lost to Boston (4-1 on the road Thursday) so we wanted to bounce back against a really good team like Winnipeg."