Russian third seed Medvedev made a shaky start but fought back in the second set, powering down five aces and breaking China's Zhang twice.
The former US Open champion paid a heavy price for double faults in the third set, however, as Zhang, ranked 42nd, came through long rallies in the tiebreak to clinch his first win over a top-five ranked opponent on grass and reach the quarter-finals.
"It was a really tough match," Zhang said. "Last time I lost to him in a third set tiebreak. When we went into a third set tiebreak today I was thinking, perfect moment for revenge."
Zhang will next face American Christopher Eubanks, who beat defending champion Alexander Bublik 7-6(5) 4-6 6-3.
German world number four Alexander Zverev overcame Italy's Lorenzo Sonego 6-4 7-6(5) after winning a close tiebreak in the second set to reach the last eight.
"Extremely happy with my performance, I'm enjoying the moment in these beautiful courts, happy with the way I'm playing," the 27-year-old Zverev said.
The second seed will next face Frenchman Arthur Fils, who defeated fellow German Dominik Koepfer 6-3 6-4.
