Johnson scored 2:25 into overtime to lift the Lightning to a 3-2 victory over the Detroit Red Wings on Thursday night that evened their series at 2-2.
The winning goal capped a stretch in which Johnson had two goals and an assist in a span of 7:51, enabling Tampa Bay to wipe out a late two-goal deficit.
"Never a doubt, was there?" Lightning coach Jon Cooper joked.
The Red Wings led 2-0 in the third period before Johnson scored with 5:26 remaining. He then assisted on Ondrej Palat's tying goal 77 seconds later.
Early in the extra session, defenceman Victor Hedman led an odd-man rush from the right side and slid the puck across the goal mouth. It deflected ever so slightly off goalie Petr Mrazek, but Johnson was able to shoot into an open net from a tough angle on the other side for his fourth goal of the series.
"I don't know how we got a 3-on-1 but we did," Johnson said. "Heddy had the puck and I was actually telling him to try and pass it to (Nikita Kucherov) in the high slot because I thought on a 3-on-1 you can get to the middle a little easier. He made an unbelievable play to me and I was able to get enough on it to get it in there."
Game 5 is Saturday at Tampa Bay.
Gustav Nyquist and Joakim Andersson scored in the second period for Detroit. Andersson's goal came in fluky fashion when goalie Ben Bishop knocked it in off the crossbar.
Tampa Bay led the league in goals during the regular season, but Mrazek shut out the Lightning in Detroit in late March, then blanked them again in Game 3. He had another shutout going Thursday until Johnson skated in on the left and beat him to the short side to make it 2-1.
"I think we'd gone probably eight periods without scoring a goal in this building but as soon as we got that one, we grew a couple inches on the bench," Cooper said. "It was like a weight off our shoulders and clearly the game changed at the moment we scored that goal."
Johnson then centred a perfect pass from the right that Palat only needed to redirect past Mrazek to tie the game with 4:09 remaining.
Detroit coach Mike Babcock said a third-period injury to Luke Glendening was crucial.
"Obviously Luke getting his hand cut and missing the rest of the game, matchup-wise with Johnson's line then got the next three goals," Babcock said. "But still, we made some mistakes. I thought we played a good game, did lots of good things. In the end, we made some mistakes at the end that they capitalized on."
The opening goal came after Detroit's Justin Abdelkader found Henrik Zetterberg near the net, and the Red Wings' captain patiently slid the puck to Nyquist for a tap-in from in front.
The Red Wings were more lucky than good on their second. Andersson's shot bounced routinely off Bishop and up in the air, but when Bishop tried to bat the puck away with his stick, he instead accidentally knocked it back off the crossbar.
The puck fell to the ice and slowly slid across the goal line, with defenceman Jason Garrison unable to clear it.
"Now it looks like a tough hole to climb out of," Cooper said. "But he shut the door after that."
After Detroit's two goals in the second, the Lightning were able to increase the pressure toward the end of that period, but Mrazek was up to the task.
His counterpart, meanwhile, became visibly upset with the officials early in the third. That's when Bishop was called for a tripping penalty, to the delight of the Detroit crowd.
But the Red Wings didn't score on that power play, and they couldn't hold the lead.
"I thought we played well," Detroit's Drew Miller said. "Obviously, the last five minutes got away from us and we lost there. You have to find the positives from this game, go back down there and be ready to play."
NOTES: Garrison returned after missing the first three games of the series with an upper-body injury. ... Bishop had 22 saves and Mrazek had 26. Johnson's goal was the only shot on goal of the OT.