Vermette scored his second game winner of the series as he hammered home a rebound from the slot just two minutes into the final period.
Chicago forward Kris Versteeg took the initial shot and Tampa goalie Ben Bishop kicked the rebound right to Vermette, who was driving hard to the front of the net.
It was the fourth goal of the post-season for Vermette who also scored the game winner in a 2-1 victory in game one.
This has been one of the closest finals in league history and game five was no different as for the third straight game the teams entered the third period tied.
The team that has won game five after a split of the opening four contests of the final has gone on to claim the Stanley Cup 16 of 23 times.
Patrick Sharp also scored and goaltender Corey Crawford made 32 saves for the Blackhawks, who are chasing their sixth Stanley Cup title in franchise history after previous wins in 2013, 2010, 1961, 1938 and 1934.
Valtteri Filppula scored the only Lightning goal and Bishop made 29 saves in his return to the net after missing game four with an undisclosed injury.
Game seven if necessary would be Wednesday in Tampa.
