Bemstrom restored the Blue Jackets to a 2-1 lead at 10:15. Nyquist redirected a stretch pass from Bean to Bemstrom, who split the defense and shot high blocker side for this first of the season.
Nelson tied it again 2-2 with 45 seconds left in the period, scoring from low in the right circle off a rebound of Aho's initial shot.
"That's frustrating," Sillinger said. "I mean, we had a lot of a lot of guys come into the lineup and step up and have that extra opportunity, but it's a matter of playing for 60 minutes. We had some momentum there at the end of the second period, but we could have been sharper getting out of the zone."
Bjork, who was called up from Cleveland of the American Hockey League on an emergency basis on Friday, scored with a slap shot from the top of the right circle to put Columbus back in front 3-2 at 9:38 of the third period.
"I didn't see it at first, but it went in so it was a nice feeling," said the 24-year-old defenseman, who signed with the Blue Jackets as an undrafted free agent on May 24.
Mayfield tied it 3-3 at 12:51 with a backhand in the slot.
"Those extra points you accumulate can be the difference between you being in a good spot in the standings and not being in a good spot," Islanders coach Lane Lambert said.
NOTES: Nelson had 10 shots on goal, all in the first two periods. … Jake Christiansen made his season debut and Gavin Bayreuther played in his second game for the Blue Jackets. The defensemen were also recalled from Cleveland after Zach Werenski (torn labrum), Nick Blankenburg (ankle) and Erik Gudbranson (upper body) were injured in a 5-2 win against the Philadelphia Flyers on Thursday.