Defending champion Alexander, 21, won 6-3 7-5 in what was the first ATP Tour meeting between the German siblings.

They had previously met on two occasions: the last at the US Men's Clay Court Championship in 2014.

"I needed a few seconds to actually bite my tongue and focus," said Mischa.

"It was very emotional for me. It was just a great day."

Alexander will play Kei Nishikori in the quarter-finals after the Japanese seventh seed defeated Canada's Denis Shapovalov 7-6 (7-1) 6-3.

Speaking about his victory over his brother, Alexander said: "We played near our best. It was unbelievable.

"I just hope it happens again and I hope it happens at later stages of bigger tournaments. I hope we meet again someday in a final."

Later on Thursday evening, the brothers then teamed up to complete their rain-delayed first-round doubles match, in which they defeated top seeds Oliver Marach and Mate Pavic 6-1 6-4.