Poole's buzzer beater, was the ninth lead change of the night, no team ever led by more than six. MI did not enter the bonus until six minutes remained in the half, and Houston only had eight fouls at that point.
John Beilein and the Wolverines will next face the victor of Sunday's matchup between the North Carolina Tar Heels and the Texas A&M Aggies.
After the game, coach John Beilein and Poole both acknowledged the team had run the winning play before in practice numerous times and were confident in executing it to completion.
Just before the game-winner, the Wolverines had chances to tie and take the lead, but narrowly missed a number of shots.
MI (30-7) advanced to its fourth Sweet 16 appearance in the last six years and marked its first 30-win season since the 2012-13 campaign. MI trailed 63-61 in the final minute, and that could have been even a wider lead if the Cougars had hit some foul shots. For the win! The three-pointer by Jordan Poole! One could say with confidence that the game was won (or lost, in Houston's case) at the free throw line.
Whistles became constant as the second half wore on, and both teams soon found themselves in foul trouble.
MI is going to Los Angeles.
Abdur-Rahkman and Moritz Wagner each scored 12 points to lead MI, and Charles Matthews and Duncan Robinson added 11 apiece.
The Wolverines have a couple of days to celebrate their big win before preparing for the next round in the NCAA tournament.
Houston fifth-year senior Devin Davis missed two crucial free throws to open the door for Jordan Poole's epic buzzer-beating 3 on Saturday night.
Abdur-Rahkman wound up 4 of 15 from the floor and 0 of 6 from 3-point range.