Jake Guentzel had a goal and an assist, Nick Paul and Mitchell Chaffee also scored and Victor Hedman had two assists to help the Lightning end a two-game skid.
Jonas Johansson made 11 saves.
Louis Crevier and Frank Nazar each had a goal and an assist, and Colton Dach also scored for Chicago, which has a season-high four-game point streak (1-0-3).
Arvid Soderblom finished with 36 saves.
In the extra period, Kucherov beat Soderblom cleanly with a hard wrist shot from the right circle.
Crevier’s goal 4:59 into the second period gave Chicago a 3-1 lead.
Paul pulled the Lightning within one with eight seconds left in the middle period, and Guentzel deflected Kucherov’s pass from the right corner to tie the score with 3.3 seconds left in regulation.
During the game, the Blackhawks sent forward Taylor Hall to Carolina in a three-way deal.
Lightning: Paul’s goal in the closing seconds of the second period swung the momentum to Tampa Bay.
Blackhawks: Hall’s departure accelerates Chicago’s youth movement. Nazar, Dach — who got his first career goal — and Crevier all have no more than a half-season of NHL experience.
Guentzel’s tying goal from the doorstep took the wind out of the Blackhawks, who had been keeping the Lighting away from the crease for most of the third period.
The Lightning outshot Chicago 40-14, including a 17-1 advantage in the third period, and had the only shot in overtime.
Lightning visit Detroit on Saturday, and Blackhawks host Minnesota on Sunday.
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