Medvedev beat Cressy 6-2 7-6 (7-4) 6-7 (4-7) 7-5 on Monday to ensure his place in the quarter-finals of the Australian Open.
The second seed is the fifth Russian man in the Open Era to reach the quarter-finals in Melbourne on multiple occasions, joining Yevgeny Kafelnikov (five), Nikolay Davydenko (four), Aleksandar Metreveli and Marat Safin (both three).
Medvedev had it far from easy against the world number 70, who reached the final of the Melbourne Summer Set earlier this month, losing to Rafael Nadal, and the match lasted three hours and 30 minutes on Margaret Court Arena.
Indeed, Medvedev was extremely tense in the fourth and what proved to be final set, as he squandered eight chances to break before finally doing so to nudge himself into a 6-5 lead.
His temper frayed at 2-2, however, with Medvedev shouting: "It's simply unbelievable how lucky he is. I've never seen anything like this in my life."
Medvedev eventually served out the win, taking the first match point on offer, but the US Open champion knew he had been in a battle.
"He really did [serve and volley] well," Medvedev said. "First set I had control, but the second set I didn't manage to break him but won the tie-break and just wanted to continue this way.
"When I lost the third [set] and when I had eight break points in the fourth set, I was like, come on. Some of them I could have won, but he played well, but on the last one I played well.
"It was not easy. If I didn't win the fourth [set] I'd have probably been in a difficult mental shape because I had so many breakpoints. Hell of a match. The fourth set was crazy."
Overall it was a deserved win for Medvedev, who made only 11 unforced errors in contrast to Cressy's 49, and even if he only took three out of 12 break points, the 25-year-old offered up just one to his opponent, which the French-born American failed to capitalise on.
Another annoyance for Medvedev was that he was again scheduled to play on Margaret Court Arena, rather than the crown jewel at Melbourne Park, Rod Laver Arena.
"I really don't know what I should do to play on centre court here," he told reporters.
Next up for Medvedev is a quarter-final tie against ninth seed Felix Auger-Aliassime.
Medvedev has defeated the 21-year-old Canadian in all three of their previous meetings on the ATP Tour, including in his successful run to US Open glory last year, and in the ATP Cup earlier this month.