Hayes started the blitz with a shot from the point that went through traffic before slipping past Binnington. Laine then scored his third goal of the series, converting a pass from Jacob Trouba.
Connor capped the blitz with a power-play wrist shot from the faceoff dot at 8:58. He added an insurance goal 14:44 into the final period.
“It was just a matter of time,” Hayes said. “It’s a start.”
St. Louis had a chance in the third, pulling within one when Tarasenko scored a power-play goal just 1:51 into the period. But Tanev and Byfuglien responded for Winnipeg, running its lead back out to 5-2 with 11:54 left.
“Tonight was not really our team, obviously,” Perron said “We weren’t happy with our effort. We didn’t play a good game. But we’ve got to give them credit.”
Laine, who had 30 goals and 20 assists in the regular season, has scored in all three playoff games. He had just one goal in his last 19 regular-season games.
Laine scored five goals in an 8-4 win in St. Louis on Nov. 24, 2018.
“We just stayed within our game and tried to play it simple,” Laine said. “We got going and just tried to keep our foot on the gas the whole 60 (minutes).”
Hellebuyck made a big stop on Pat Maroon just seconds before Tanev’s goal.
Binnington made a trio of saves in the opening 5:45 to keep the game scoreless. He denied Bryan Little, Hayes, and Mathieu Perrault. Binnington stopped 50 of 54 shots over the first two games.
“The biggest thing is we didn’t play our game tonight,” Tarasenko said. “It was not our best game out there. It’s on us, and we’ll handle it tomorrow.”
NOTES: Blues D Robert Bortuzzo suffered a cut on his hand that required seven stitches in the third period of Game 2, but played on Sunday. … Winnipeg is 1-10 in playoff games decided by one goal, including a 1-4 mark last season. … The Blues failed on their first seven power-play attempts in the series prior to Perron’s first-period goal. … The Jets were the last team in the playoffs to record a third-period goal.
Game 4 of the series is set for Tuesday night in St. Louis.