The Jets were dominating play to that point, holding a 19-5 edge in shots before the Barzal goal.
Over the last four games, the Jets - who coming into the night were the least penalized team in the NHL - have allowed five goals on the PK.
"It just seems when it rains, it pours. Sometimes you try a little bit too hard and it's almost worse. The confidence is a little bit low on that right now," said Wheeler. "We have to start from the bottom and rebuild ourselves on the penalty kill, be committed to eating some pucks and doing whatever it takes to keep the thing out of our net."
The Islanders forward wasn't done there, however. With time winding down in the middle frame, a dump in from Josh Morrissey was knocked down at the New York blue line by Johnny Boychuk. Anders Lee quickly got the puck up to Barzal, who kept on a two-on-one and beat Hellebuyck on the stick side for a 2-1 Islanders lead.
It was the second time in the last two games the Jets had allowed a goal in the final minute of a period, but head coach Paul Maurice said it's not because the Jets are sitting back.
"The goal at the end of the second clearly hurts because it's a controlled situation and we have possession of the puck. That's a tough one," Maurice said. "But there is still lots of time on the clock and lots of opportunities to tie that game."
With the Jets pressing in the final minutes, Josh Bailey put the insurance marker on the board with 27 seconds left on the clock to round out the scoring.
Winnipeg has scored the first goal in each of the three games on the home stand, but have come up empty in terms of wins in that department.
"We're not sitting back in these games. We're not defending a 1-0 lead from the second period on," said Maurice. "It's not a function of us not having a killer instinct."
The next chance to snap the skid comes on Sunday against the Edmonton Oilers.