The fourth seed eventually beat Filip Krajinovic 6-3 6-3 4-6 3-6 6-0.
Medvedev repeatedly yelled at his box as he went 4-1 down in the fourth – with coach Gilles Cervara eventually picking up his bag and leaving.
He did not return to see Medvedev dial back in to dominate the deciding set.
“He said just before leaving that he’s sure I’m going to win the match, but he’s going to leave to let me be more calm,” Medvedev said of Cervara’s exit.
“Sometimes maybe I will disagree but this time for sure it was a good thing to do.
“Today it helped, and definitely we’re going to talk about it a little bit, but there is not a big deal.”
Medvedev, among the favourites to challenge defending champion Novak Djokovic, yelled in French, Russian and English as the match against the Serb slipped from his grasp.
He also complained about the spider-camera at Melbourne Park, saying it was obstructing his toss on serve, and at one point shouted: “This Australian Open sucks.”
He received a medical time-out in the fourth set after complaining of buttock pain and then went on to win the final set without dropping a game in just 25 minutes.
Medvedev, who won the season-ending ATP Finals in 2020, has often caught attention for his on-court antics.
He was booed throughout the US Open in 2019 where he reached the final, and he later admitted that the crowd spurred him on.
“Sometimes I’m a very temperamental person on the court so it can still get out, and usually it doesn’t help me to play good,” he said.
“Now I think I have made big steps already working on my mental strengths.”
There are no crowds at the tournament after the state of Victoria entered an emergency five-day lockdown on Saturday.
Medvedev will play Mackenzie McDonald next after the American beat Lloyd Harris of South Africa 7-6 (9-7) 6-1 6-4.
