After further review following the game, Campoli was proven right. His initial shot went in.
Campoli's short-handed tally capped a second period in which the Islanders took a 3-0 lead, connecting three times within 11:07.
Richard Park and Bill Guerin had the other goals for New York, which entered with the fewest points in the NHL.
The Blue Jackets came away with a point after a furious third period in which they erased a 3-0 deficit. R.J. Umberger scored Columbus' final two goals after defenseman Marc Methot started the comeback.
Columbus, the last-place team in the Central Division, is 1-3-2 in its last six. The Blue Jackets were nearly the second team in three nights to get out of Long Island with a win after trailing by three goals in the third. Montreal used a four-goal frame Saturday to beat the Islanders 5-4 in regulation.
Umberger tied it with his second of the night with 8:58 left in the third.
Joey MacDonald, subbing for injured goalie Rick DiPietro, was on track for his first NHL shutout, but those hopes were quickly dashed when Methot and Umberger scored 1:12 apart in the first five minutes of the third.
After a scoreless first period in which the Islanders were outshot 13-7, New York broke out despite being whistled for all four penalties.
The Islanders made it 2-0 when Guerin got the puck from Park just as he left the penalty box and skated alone into the Columbus zone. Norrena came out to cut down the angle, but Guerin shifted to the right and put the puck in at 10:16.
The Blue Jackets were on another power play when Columbus defenseman Christian Backman was about to be called for a penalty.
New York put the pressure on during the delayed call, and while players piled up in front, Campoli drifted into the slot and slammed in a loose puck with 5:45 left.
Campoli, who missed a large chunk of last season due to a shoulder injury, scored for the first time since Dec. 29, 2007 - a span of only 14 games.
Columbus needed only 28 seconds of a power play to make it 3-2 at 3:44 of the third. Umberger got to a rebound in front and scored between MacDonald's pads with a second whack at 4:56.
Park gave the Islanders a 1-0 lead at 3:08 of the second.
Fredrik Modin had a chance to tie it moments later, but his shot from just outside of the crease went wide of an open net.
Notes: The Blue Jackets were 1-for-7 on the power play, including a failed two-man advantage for 56 seconds. New York was 0-for-2.
... Columbus D Rostislav Klesla, who played every game last season, was sidelined by an undisclosed injury. ... Islanders LW Sean Bergenheim sat out because of an illness. ... Modin returned from a six-game absence (groin) and had five shots in the first period.
