Wawrinka secured the only break of the match in the third game of the opening set to edge in front, before holding to love to seal the set in the 10th game.
Following an even second set, which saw no break point opportunities, the Swiss took the tiebreak on his second match point in order to advance to the last eight.
Greek No. 3 seed Tsitsipas struggled to exert authority on the lowly-ranked Dzumhur, who took the first set with an ace down the T.
Tsitsipas managed to level the scores but struggled again in the decider and, after saving match points at 4-5, eventually dropped serve to love with a forehand long to give Dzumhur the win.
The Russian, who was crowned champion at last week’s Sofia Open, defeated his French opponent 7-6 (2), 6-2 to make the last 16.
Medvedev had been forced to save the first set after squandering a comfortable advantage to set up Chardy at 5-4, but he found a timely break to restore parity then secured the crucial first set tiebreak.