Artemi Panarin, Braden Schneider and Chris Kreider scored for the Rangers, and Mika Zibanejad had two assists. Jonathan Quick finished with 20 saves in New York's third straight loss (0-1-2).
Fantilli scored two goals 26 seconds apart early in the second period to give the Blue Jackets a 3-1 lead.
Schneider and Kredier scored short-handed goals 42 seconds apart to tie the score, but it was all Blue Jackets after that.
Olivier and Fabbro scored late in the middle period to give Columbus a 5-3 lead.
Johnson made it 6-3 midway through the third when his attempt on the rebound of a shot by Olivier went off Rangers defenseman Zac Jones and past Quick.
Fantilli finished the hat trick with 8:09 remaining,.
Takeaways
Blue Jackets: Columbus moved one point ahead of Ottawa for the first wild card in the Eastern Conference.
Rangers: New York remained outside of a playoff spot, one point behind the Senators for the second wild card.
Key moment
Fantilli got a pass from Kirill Marchenko from in front of Quick and fired a shot from between the circles past Quick for the 20-year-old center's second hat trick this season.
Key stat
Schneider and Kreider scored short-handed goals, giving the Rangers a league-high 13 on the season.
Up next
Blue Jackets visit Devils on Tuesday, and Rangers play at Winnipeg to open a three-game trip.
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AP NHL: https://www.apnews.com/hub/NHL
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The Associated Press created this story using technology provided by Data Skrive and data from Sportradar.