Alex Vlasic's shot from the high slot hit the goal post, with Bedard snapping in the rebound from the left side.
Frank Nazar and Tyler Bertuzzi each had a goal and an assist for the Blackhawks (25-29-11). Spencer Knight made 29 saves for the Blackhawks after missing three games because of illness.
Chicago defeated Utah twice in four days, winning 3-2 in overtime at United Center on Monday, and went 4-0-0 against the Mammoth this season.
Karel Vejmelka made 20 saves for the Mammoth (34-26-6), who are 0-1-2 in their last three games.
After a scoreless first period, Dylan Guenther gave the Mammoth a 1-0 lead at 5:47 of the second period. Logan Cooley carried the puck up the ice after a turnover by Chicago’s Andre Burakovsky and passed across to Guenther, who put the puck over Knight’s right shoulder from the right face-off circle.
Bertuzzi tied it at 2:18 of the third period with the Blackhawks on a 4-on-3 power play. Bertuzzi moved to the right side of the crease and redirected a pass from Bedard from the left face-off dot.
Nazar gave Chicago its first lead 2-1 at 9:17. Bertuzzi's shot from the right circle rebounded off Vejmelka. Teuvo Teravainen kicked the puck over to Nazar, who swept the puck in from the left post after circling the net.
JJ Peterka tied the game 2-2 at 13:45. Michael Carcone stripped Vlasic of the puck in the offensive zone and passed over to Peterka, who put it between Knight's pads from the right circle.
