Bowman, an undrafted free agent, made his NHL debut on Thursday against the New York Islanders.
Brandon Saad, Noah Hanifin and Tomas Hertl also scored for the Golden Knights (8-4-5), who were 0-2-2 their previous four games. Akira Schmid made 21 saves, and Reilly Smith and Pavel Dorofeyev each had two assists.
Philip Broberg scored, and Joel Hofer made 29 saves for the Blues (6-9-4), who lost 6-5 in a shootout to the Philadelphia Flyers on Friday.
Saad’s first of the season in his first game against the Blues since being waived by St. Louis last season at 12:52 of the first period made it 1-0 after Matthew Kessel’s giveaway and shot from the slot.
Bowman’s power-play goal at 14:58 made it 2-0 on a one-timer off a quick pass from Dorofeyev to the crease.
Hanifin’s first of the season 36 seconds into the second period extended the lead to 3-0, a long range shot from the blue line.
Hertl scored on a breakaway at 11:20 of the third period to make it 4-0 after the Blues fumbled the puck at the offensive zone blue line. Hertl has scored in three straight games.
Broberg ended Schmid’s shutout bid when he scored at 15:57 to make it a 4-1 final on a shot from the point.