It's the third straight year Butler (20-8, 12-3 MCC) has ousted Green Bay (20-11, 9-6) from the tournament. The second-seeded Bulldogs will play top-seeded Detroit on Tuesday night for the MCC's automatic bid to the NCAA tournament.
Hicks finished with 17 points. Andy Hirschy led Butler with 23, while Mike Marshall added 13 and Rylan Hainje had 11.
B.J. LaRue, whose 3-pointer forced the third overtime, led Green Bay with 29 points. Jerry Carstensen had 10 for the Phoenix.
LaRue tied the game at 57 on his 3-pointer with 15.8 seconds left in the second overtime, scoring his first basket in more than 12 minutes even though Hicks was practically draped on top of him. But the final overtime belonged to Butler, which has now beaten Green Bay in seven straight meetings.
After Hainje converted on a three-point play on Butler's first possession of the third overtime, Ryan Mueller tied it with a three-point play of his own. Hicks scored a rebound basket and Hainje made a free throw to put the Bulldogs up 63-60 with 2:53 left.
Carstensen scored on an uncontested layup to pull the Phoenix within 63-62, but Hirschy hit a jumper with 1:01 left. Then Hicks stripped LaRue and made the game-winning layup with 46 seconds left. He gave the Bulldogs some more breathng room with a free throw with 16 seconds left.
LaRue made one more 3-pointer with 1.2 seconds left, but Green Bay didn't have enough time to get the ball back for another play.
The Phoenix blew a 10-point first half lead, but they were also hurt by fouls. Green Bay was called for 22 fouls compared with Butler's 11, and the Phoenix went to the free throw line just four times in the entire game. Butler made 22 trips.
Green Bay also was outrebounded 41-31.
Ryan Borowicz, who was 0-for-2 in the first 39 minutes of the game, drilled a 3-pointer with 24 seconds left in regulation to tie the game at 50. Hainje had a chance to win it, but his jumper at the buzzer went wide, sending the game into the first overtime.
Hirschy hit a jumper and Hainje made one free throw to give Butler a 53-51 lead, only to have Borowicz came through with another huge shot, knocking down his second 3-pointer with 2:24 left in the first overtime. Hicks tied the game at 54 on a free throw with 30 seconds left, but missed the second shot.
LaRue put up a jumper with two seconds left, but the ball hit the rim and bounced off.
Marshall made the first of two free throws and Hirschy added two from the foul line to give Butler a 57-54 lead with 2:44 left in the second overtime.
Green Bay missed its next two shots, but then LaRue came through with the 3-pointer that forced the third OT.
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