Rayvonte Rice added 19 points, 14 rebounds, eight assists and four steals for the Bulldogs (13-9, 6-5 Missouri Valley).
Garrett Stutz scored 27 points and Joe Ragland 25 for the Shockers (18-4, 9-2), who lost for the first time in seven road games this season and fell out of a first-place tie in the conference with Creighton, which defeated Bradley on Saturday.
Kraidon Woods made a layup for Drake with two seconds remaining in regulation to knot the score at 63-all. Alexander's 3-pointer gave the Bulldogs an 82-79 lead with 19 seconds remaining in the second OT, but Ben Smith matched it for Wichita State with eight seconds left.
Jeremy Jeffers scored 11 points for Drake.
Toure' Murry had 16 points and 10 rebounds for the Shockers, whose eight-game winning streak was snapped.
5-star guard Max Christie commits to Michigan State basketball
Five-star guard Max Christie is committing to Michigan State.
Alabama agrees to play 3 games with Memphis
Coach Penny Hardaway and Memphis will play Alabama three times over the next three seasons with two of those games in Memphis.
Louisville halts men's basketball activities after 2 test positive
Two members of the Louisville men's basketball program have tested positive for the coronavirus and have been quarantined, while the team has suspended activities.