Jordan Binnington made 25 saves for St. Louis (26-8-6), which has outscored its opponents 33-16 during the streak, including a sweep of a home-and-home with the Jets following a 5-4 overtime win at Winnipeg on Friday.
Jordan Kyrou had two assists for his first multipoint game in the NHL.
WATCH: [All Jets vs. Blues highlights]
"We're just finding different ways to win," said Schwartz, who extended his point streak to seven games (four goals, seven assists). "Our special teams has been good. I think we're just aggressive. You look at our forwards backchecking, our D have such tight gaps. We're just frustrating other teams and making it hard on their top players and we're spending some time in the O-zone and kind of wearing teams down. We're playing tight, aggressive and together, and it looks pretty quick and fast that way."
Nick Shore scored, and Connor Hellebuyck made 24 saves for Winnipeg (21-15-3). The Jets are 2-5-1 in their past eight games.