Kucherov, who has 12 points (eight goals, four assists) and is tied for the League scoring lead with Lightning center Steven Stamkos (two goals, 10 assists), can equal the mark set by Edmonton Oilers center Wayne Gretzky, who scored at least one goal in each of the first eight games of the 1983-84 season.
Pittsburgh Penguins center Mario Lemieux scored at least one goal in the first 12 games of the 1992-93 season, and New York Islanders forward Mike Bossy scored at least one goal in the first 10 games in 1984-85.
The Lightning are looking for their best start since going 7-0-1 in 2003-04.
The Blue Jackets, aiming for their fifth straight win, can set a Columbus record with a 6-1-0 start, which would surpass their 5-2-0 start in 2009-10.