Patrik Laine buried his 23rd goal of the season from the face-off dot at 15:56 to tie the game at 2-2.
Mathieu Perreault darted out of the penalty box and potted a goal at 19:42 of the second on a breakaway to give the Jets a 3-2 lead heading into the third period.
With time running out, the Blackhawks pulled Crawford for the extra attacker. Erik Gustafsson, who returned to the ice tonight after missing two games due to an illness, rifled a slap shot past Brossoit to tie the game at 3-3 with 7.5 seconds left in regulation.
Scheifele put a halt to the celebrations with his second of the night and 20th on the season just 50 seconds into overtime.
THE CAPTAIN LEADS THE WAY:Toews' goal in the first period was his 15th of the season, which tied him with Patrick Kane for the team lead. The last time Jonathan Toews had 15 goals in a season before the new year came in 2013-14. He reached 15 on Dec. 27, 2013, which was his 40th game that season. It took him until his 34th game to reach that mark this year. He then overtook Kane with his team-leading 16th of the season at 13:07 of the second.