Mies, who is ranked 19th nationally in singles, scored a 6-3, 6-2 victory over 45th-ranked Yannick Hanfmann of Southern Cal. Mies, who has already qualified for All-American honors in singles, improved his season record to 21-9 in singles.
"I think I played a very good match today," Mies said. "I had two tough matches in the first two rounds that went three sets so it was good to save some energy for the next round.
"I'm really pleased with my match today," he added. "I really thought it was a big achievement to go to the Sweet 16, but to go to the quarter-finals feels even better. I hope I'm not finished yet and that I can go deep in the tournament."
On Saturday at the Khan Tennis Center he will take on 11th seed Sebastian Fanselow of Pepperdine in the quarter-finals of the 64-player draw at the University of Illinois. The match is scheduled to start at noon CDT.
Mies and his doubles partner, junior Daniel Cochrane, rallied after dropping the first set 6-4 to 60th-ranked Lucas Ana and Victor Valente of Georgia State. The sixth-ranked Tiger duo spanked their opponents 6-0 in the second set and took the match with a 6-4 win in set three to advance to Saturday's quarter-finals round vs. Henrique Cunha and Raphael Hemmeler of Duke, who are ranked No. 2 nationally.
Coach Eric Shore said he liked what he saw on Friday, the first time in school history that the Tigers advanced a singles player and a doubles team into the quarter-finals at the same time.
"What a day," Shore said. "We found a way to get it done. Andy was solid as a rock in singles today. He was ripping the ball. He's playing better and better as the tournament goes on. He's gaining confidence and hitting the ball really clean, but you've got to raise your level as you go on in this tournament.
"Then in doubles we just found a way to win," Shore added. "That (Georgia State) team was tough. We just found a way to get it done. We were up 3-1 and 5-3 in the third set, got broken both times, and then broke back to win it."