Justin Faulk and Jake Neighbours also scored for the Blues, and Torey Krug had two assists.
Jake Oettinger made 24 saves for the Stars.
Faulk gave St. Louis a 1-0 lead with a wrist shot from the right circle at 5:39 of the first period.
Thomas made it 2-0 when his shot banked off Thomas Harley’s skate and past Oettinger at 1:41 of the third period, then scored on a power play at 18:16 to give the Blues a 3-0 lead.
Neighbours also scored a power-play goal at 19:29 for the 4-0 final.
