Brayden Schenn had two assists for St. Louis (27-14-5), which is 6-0-2 in its past eight games against Chicago. Ville Husso made 15 saves in his sixth start in the past eight games and is 8-1-0 at home this season.
"I think we did a really good job, especially the F1 and F2 [forwards] coming in and getting a stop to the play, getting in quick and getting the puck back," Sundqvist said. "The forecheck was really good today and it's a key for our game to be successful. Our forecheck game is very important. When it works, then we're really dangerous."
Dylan Strome scored, and Marc-Andre Fleury made 26 saves for Chicago (17-24-7), which was held to 16 shots, a season low.
"I felt pretty good coming in here," Blackhawks coach Derek King said. "I thought if we put a solid effort in, we compete with these guys and at least give ourselves an honest chance.
"That's a good hockey team, we know that. We knew it was going to be a challenge, but that's not good enough. I've got to watch my words here, but we just can't do that. You can't put an effort like that out and maybe steal a game from somebody. That's not going to happen."