The Blues won their sixth in a row and maintained their hold on the sixth playoff position in the Western Conference. Minnesota is in the seventh spots, just two points in front of Detroit.
Elliott made 23 saves in recording his third shutout of the season and the 21st of his 6-year career. He established a franchise record last season by putting together a shutout streak of 241 minutes, 33 seconds.
Roman Polak scored his first goal in 3 seasons midway through the first period and Elliott protected the 1-0 lead until Andy McDonald tallied on a backhander 9:30 into the third.
The six-game winning streak is a season best for the Blues.
Niklas Backstrom stopped 18-of-20 shots in what was the Wild's fifth loss in six games. They have managed only six goals in that stretch.