Lautier-Ogunleye had six rebounds and dished out four assists. Van Bree was 6 of 9 from the floor, making 3 of 5 from long range.
The Braves, who never trailed, held a 31-19 lead at the break and finished the game on a 27-6 run. Chicago State never threatened.
Bradley made 24 of 46 (52.2 percent) field goal attempts while limiting Chicago State to just 16-of-59 (27.1 percent) shooting.
Bradley shot 43.5 percent in the first half while limiting Chicago State to 21.5 percent.
Trayvon Palmer had 21 points to lead Chicago State (3-5).