A trio of late third period goals and a 34-save performance from David Rittich iced the victory for the Heat, who have been able to claw their way back into the five-game series twice after falling behind in Games 1 and 3.
"We're a thorn in the side, for sure, and we've been that way for a while," Heat head coach Ryan Huska told the media following Sunday's win. "There's a real strong belief in our group. Even when we got ourselves down in the third period, our bench didn't change at all. There's 100% belief that we were going to win the game.
"It may have been a little more stressful than we would've liked, but we got the job done and that's what's important. That's what we needed to do. Find a way to get the game in San Jose. We have one more game to look forward to and we have to find a way to win on the road now."
The Barracuda opened the scoring with a goal from forward Daniel O'Regan just 58 seconds in and outshot the Heat 10-6 in the first period.
The Heat took a 2-1 lead in the second period with goals from Hunter Shinkaruk and Garnet Hathaway but a late tally from Barracuda forward Buddy Robinson evened things up after 40:00 of play.
San Jose pulled ahead in early on in the third period thanks to defenceman Tim Heed's one-timer from the point that beat Rittich high glove side. The Barracuda clung to their lead until Heat rookie Andrew Mangiapane netted the equalizer at 14:55, taking a pass from Brett Kulak and wristing a shot past netminder Troy Grosenick in tight.
Linden Vey would play the hero just a couple of minutes later when he potted the game-winning goal at 17:04 of the third period. Shinkaruk's wrap-around attempt went wide but Vey was perched at the side of the net and was able to put a backhand shot over Grosenick's shoulder.
"At times, it's frustrating. I thought from the second period on, we carried the play and started taking it to them. For them to get a goal like that early [in the third], it's a little bit tough, but we stuck with it," Vey stated. "It shows you're a good team when you can keep coming back and win games like that."
Vey added an empty-netter at 18:38 and now has four goals in the postseason.