Suter recorded an assist and three hits in Thursday's 4-3 loss to the Sharks.
Suter logged an assist and went plus-3 in Monday's 5-2 win over the Rangers.
Suter logged an assist, three blocked shots and a plus-2 rating in Saturday's 5-2 loss to the Canadiens.
Suter signed a one-year, $775,000 contract with the Blues on Wednesday.
Suter will be bought out of the last year of his contract by the Stars, Jeff Marek of Sportsnet reports Thursday.
Suter notched an assist and went plus-2 in Wednesday's 5-2 win over the Coyotes.
Suter notched an assist and blocked two shots in Saturday's 4-1 win over the Kings.
Suter posted two assists and a plus-2 rating in Thursday's 9-2 win over the Predators.
Suter provided a pair of assists, two hits and four PIM in Saturday's 6-2 win over the Devils.
Suter logged an assist, three blocked shots and a plus-4 rating in Wednesday's 7-2 win over the Wild.