Brad Boyes scored the only goal of the game on assists from T.J. Oshie and Andy McDonald for the Blues, who had dropped four of six coming into the contest.
Cristobal Huet made 22 saves in the loss for the Blackhawks, who had won four of five coming into the game.
Chicago wrapped up a season-high eight-game road trip with a mark of 5-3-0.
The Blues scored while skating on a 4-on-3 power play. Oshie had the puck in the high slot and dished it to the low right side for McDonald, who threw it over the left circle for a one-timer by Boyes just 57 seconds into the third.
Chicago went on the attack quickly after the goal and almost tied it with several whacks at the net during a scrum, but Mason was able to cover it up with the glove.
The Blackhawks had opportunities to tie the game as the team was awarded a pair of power plays late in the contest, but the Blues defense did their job and Mason turned aside the few shots that got through.
Chicago pulled Huet in the final minute of play, but it didn't help as St. Louis held on for the win.
Each goaltender needed to make just five stops in the first period to keep the game scoreless.
Huet stopped eight shots in the second period while Mason turned aside six attempts.