Tyler Seguin also scored, and Jake Oettinger made 25 saves for Dallas (8-4-0), which was playing its first game since back-to-back losses against the Florida Panthers at NHL Global Series Finland presented by Fastenal on Friday and Saturday.
Tyler Bertuzzi scored, and Arvid Soderblom made 37 saves for Chicago (5-9-1), which lost 4-1 to the Detroit Red Wings on Wednesday.
Steel gave Dallas a 1-0 lead at 11:06 of the first period with a snap shot from the top of the right circle.
Seguin made it 2-0 at 10:15 of the second period, beating Soderblom with a snap shot from a tight angle below the left circle.
Bertuzzi cut the lead to 2-1 with a power-play goal at 9:00 of the third period when he deflected a Connor Bedard shot at the front of the net.
Stankoven scored an empty-net goal at 19:14 for the 3-1 final.