With Game 5 on Saturday night, Tampa Bay was potentially 24 hours away from its second championship in franchise history after winning it in 2004.
On the winning power play, Shattenkirk told Hedman to get him the puck and he'd find a lane.
The shot got through, setting off a raucous celebration as Lightning players hopped off the bench to swarm Shattenkirk.
Even before OT, The Lightning carried the play for much of the night and showed the depth and talent that has made them a Cup contender for several years.
The Lightning survived a penalty kill of their own minutes early in OT after defenseman Mikhail Sergachev was whistled for holding Tyler Seguin.