After that, the lead changed hands six times and the game tied five times before Tony Wills' 3-pointer with 1:22 put Illinois State in front 63-60. Lee made four free throws from there while the Bulldogs (5-9, 0-2) missed a pair of 3-pointers in the final 30 seconds.
Drake led 32-22 at halftime as the Redbirds shot just 26.5 percent before intermission.
Lee had 15 points and Deontae Hawkins 12 for the Redbirds, who shot 61 percent in the second half.
Illinois State is 2-0 in the MVC for the first time since 2008-09.