Nikolay Kulemin scored the go-ahead goal – after John Carlson cancelled out John Tavares’ opening goal in the first period – and then Cal Clutterbuck made sure of the victory with 53 seconds remaining.
The win ties the series at 3-3 and there will now be a winner takes all clash for a place in the second round of the play-offs.
The Tampa Bay Lightning will be hoping they can replicate that pattern after they went 3-2 down in their series with the Detroit Red Wings on Saturday.
But they will have to show a massive improvement if they are to redress the balance after Detroit battered them 4-0, courtesy of strikes from Riley Sheahan, Drew Miller, Pavel Datsyuk and Danny DeKeyser.
The Chicago Blackhawks and the Calgary Flames are both already in the next round after they both clinched their respective series 4-2 with wins on Saturday.
Calgary notched four unanswered goals in the third period to help them to a 7-4 win over the Vancouver Canucks on the night, while Chicago ensured their progress by edging the Nashville Predators 4-3 at United Center.