Gunnarsson scored 3:51 into overtime for a 3-2 win against the Boston Bruins in Game 2 at TD Garden on Wednesday that evened the best-of-7 series. Game 3 is at St. Louis on Saturday.
St. Louis was 0-13 in the Cup Final, including Game 1 of this series (4-2 on Monday).
"I don't score too many, but nothing comes even close," said Gunnarsson, whose goal was his first in 57 Stanley Cup Playoff games. "It's a pretty good feeling right now."
[WATCH: Blues vs. Bruins Game 2 highlights | Complete series coverage]
Gunnarsson told Blues coach Craig Berube during a quick exchange in the bathroom between the third period and overtime that he felt he needed one more chance after his slap shot hit the right post with 1:57 remaining in the third.
During a delayed penalty, the Blues kept possession and Gunnarsson scored on a slap shot from inside the blue line.
"First game, we weren't happy; today we came out flying and I think we played a great game for 60-plus minutes," the defenseman said. "That's just the team we are. We come back like that. We never give up. For me to put it in there and get the winner, it's a great feeling."
Tuukka Rask made 34 saves for the Bruins, who had their eight-game winning streak end. It was their first loss since April 30.
"Probably wasn't our best game today," Rask said. "I think, especially in the playoffs, the better team always wins. They were definitely the better team."
Video: STL@BOS, Gm2: Blues, Bruins score 40 seconds apart
St. Louis got game-tying goals from Robert Bortuzzo (at 9:37) and Vladimir Tarasenko (at 14:55) in the first period, each after a Bruins goal by Charlie Coyle (4:44) and Joakim Nordstrom (10:17).
Jordan Binnington made 21 saves, including 18 straight after allowing Coyle's power-play goal on the first shot he faced, and to Nordstrom on Boston's fifth shot. Binnington is 6-2 with a .935 save percentage in games after a loss in the playoffs.
"The boys played a great game, a disciplined game and played as a team for 60 minutes, or more than 60 minutes, I guess," Binnington said. "I think we deserved that one."
Boston, which has scored at least once with the man-advantage in six straight games, didn't score on its next four power plays after Coyle's goal, including one it received with 6:38 remaining in the third period when St. Louis center Brayden Schenn took a slashing penalty.
"It's on us to execute better at the end of the day and move a little bit more," Bruins coach Bruce Cassidy said. "I thought our whole game was like that. We didn't have as much energy it seemed with the puck to create offense 5-on-5 and on the power play."
Video: STL@BOS, Gm2: Tarasenko puts home second opportunity
Boston had to play with five defensemen after Matt Grzelcyk was injured when he was boarded by Blues forward Oskar Sundqvist at 17:57 of the first period. Sundqvist received a minor penalty.
"You scout enough and see enough video to know what the other team is all about, so you've got to play like you have a chance to win," Rask said. "Obviously, [Grzelcyk] going down in the first we are down to five [defensemen], so you've got to simplify things. They were just hard on us, so we couldn't get any room and off our game."
St. Louis felt it was able to wear down Boston because it was missing a defenseman, and that was a big reason the Blues controlled the game in the third period and dominated overtime, outshooting them 4-0.
"We kind of worked them, kind of broke them down," Blues center Ryan O'Reilly said. "I thought it gave us an advantage and we came out and had a bit more gas. As you see, I thought we outplayed them in that overtime and got the big goal."
Video: Clutch Performance: Binnington bounces back in Game 2
They said it
"Berube came in and said that he used the [bathroom] after the third period, and Gunnarsson came and stood next to him. And all Gunnarsson said to him was, 'I just need one more chance.' It's true, apparently. It worked out." -- Blues center Oskar Sundqvist
"Yeah, I can't deny that. That's where it happened. It makes it even more fun, I guess. It's a good story." -- Blues defenseman Carl Gunnarsson on his conversation with coach Craig Berube
"We need to be better. Personally, I wasn't good the last two games, so we can't be playing like that." -- Bruins forward Brad Marchand
Video: STL@BOS, Gm2: Cassidy on Blues' urgency, losing in OT
Need to know
Tarasenko has scored in four straight and has an eight-game point streak, tying Brett Hull (1990) and Gary Sabourin (1969) for the second longest in Blues playoff history. Tony Currie had a nine-game point streak in 1981. … Grzelcyk went to the hospital for tests. Cassidy did not have an update on his condition. … The Bruins' top line of Marchand, Patrice Bergeron and David Pastrnak has combined for two points, neither at even strength. ... St. Louis was swept in the Cup Final in 1968, 1969 and 1970 (Montreal Canadiens twice, Bruins).
Game 3 of Stanley Cup Final at Enterprise Center on Saturday (8 p.m. ET; NBCSN, CBC, SN, TVAS)
Video: Blues get first-ever Cup Final win, even series