Soderblom was playing for the first time since Jan. 29, a 6-2 loss to the Pittsburgh Penguins. The shutout came in his 104th NHL game.
Teuvo Teravainen, who helped Team Finland win the bronze medal at the Olympic Winter Games Milano Cortina 2026, scored a power-play goal and a short-handed goal for the Blackhawks (23-28-9), who ended a three-game losing streak. Nick Foligno and Landon Slaggert also scored.
Karel Vejmelka made 24 saves for the Mammoth (31-25-4), who have lost two of their three games since returning from the Olympic break.
Teravainen gave the Blackhawks a 1-0 lead with a power-play goal at 19:06 of the first period, collecting a rebound and beating Vejmelka on the blocker side.
Foligno scored his 250th NHL goal at 11:38 of the second period, picking up a loose puck in front of the net and beating Vejmelka with a backhand deke to extend the lead to 2-0.
Slaggert scored just 1:29 later at 13:07, firing a wrist shot from the slot that went off the glove of Vejmelka and into the net to make it 3-0.
Teravainen scored short-handed at 1:25 of the third period, sending a wrist shot past Vejmelka for the 4-0 final.