The Jets trail the best-of-7 series 2-1. Game 4 is here Tuesday.
"We're building every shift, every game throughout the series," Connor said. "We're getting closer to our game, and it's pretty dangerous."
WATCH: [Jets vs. Blues Game 3 highlights | Complete series coverage]
Patrik Laine and Dustin Byfuglien each had a goal and an assist, and Connor Hellebuyck made 26 saves for the Jets.
"We just stayed within our game and tried to play it simple," said Laine, who has a goal in each game in the series after scoring one goal in his final 19 regular-season games. "We got going and just tried to keep our foot on the gas the whole 60 (minutes)."
David Perron, Vladimir Tarasenko and Alexander Steen scored, and Jordan Binnington made 23 saves for the Blues, who won Games 1 and 2 in Winnipeg and had won their final seven regular-season home games.
"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, they played a good game as well. We didn't respond enough."
The Jets scored three second-period goals to take a 3-1 lead. Kevin Hayes tied it 1-1 at 4:57 on a shot through traffic from the blue line. It came after Binnington made a series of saves in the first period, including close-range attempts from Bryan Little 2:03 into the game and Mathieu Perreault at 5:55 of the first period.
"The goalie has been playing great, so we just tried to get a greasy one," Hayes said of the Blues rookie. "I threw it on net and luckily, it went in."