Jansen Harkins scored his first NHL goal had an assist for the Jets (27-23-5), who won for the second time in eight games, each against the Blues.
"At the end of the day, handling the win is key," Copp said. "We're going to be in a lot of tight games like that down the stretch like that where it's tied with less than 10 minutes to go and we need to be comfortable in those games and win those games."
WATCH: [All Jets vs. Blues highlights]
The Blues (32-15-8), who are 2-5-1 in their past eight games, were 10-0-1 in their prior 11 home games.
"First period we didn't play well, but we played solid after that, lots of chances," St. Louis coach Craig Berube said. "We haven't solved [Connor] Hellebuyck good enough yet last two games."
Hellebuyck, who made 35 saves for Winnipeg, made 38 saves against St. Louis in a 5-2 win on Feb. 1.
"Your goalie is going to have to be the deciding factor and he may have been the deciding factor for us," Jets coach Paul Maurice said.
The Blues tied the game with two second-period goals in 2:20. Colton Parayko scored a power-play goal at 11:16 to make it 2-1, and Carl Gunnarsson scored at 13:36 to make it 2-2.