Kucherov was given a major penalty and ejected for hitting Nutivaara in a defenseless position with 4:26 remaining in the lopsided defeat.
Game 3 of the series is scheduled for Sunday in Columbus.
Tampa now is fighting from behind, with the Blue Jackets taking a commanding 2-0 series lead in Friday night's Game 2 of the first round of the Stanley Cup Playoffs.
But Victor Hedman wasn't one of them.
Lightning head coach Jon Cooper said he didn't see the hit and had intentionally not reviewed it before his post-game news conference.
Now, Kucherov is not known as a dirty player and has not been hit with a suspension before for such a hit, but in last year's playoffs he faced one when the Lightning took on the Devils.
He has zero points through two games against Columbus though, with Steven Stamkos (98 points during the regular season-45 goals, 53 assists) and Brayden Point (92 points during the regular season-41 goals, 51 assists) each also putting up doughnuts in the scoring column for Tampa Bay thus far in the series. He led the National Hockey League in both assists and points.
The Blue Jackets, who have never won a playoff series, coughed up a 2-0 series deficit to the eventual Cup champion Washington Capitals a year ago.
However, through two games of the first round Kucherov has yet to record a point.