The Russian third seed was in the zone to win 6-3, 6-4, 6-3 and set up a clash against Portugal's world number 69 Nuno Borges, who upset Bulgarian 13th seed Grigor Dimitrov in four sets.
It was a vastly different match from his late-night escape from two sets down against Finland's Emil Ruusuvuori in the second round, a contest that finished at 03:40 on Friday.
Medvedev admitted the early-hours finish had taken its toll, saying he had not got to bed until 07:00.
"It was not easy, I'm not feeling fresh, I'm not feeling 100 per cent," said the Russian, who lost to Novak Djokovic in the 2021 Melbourne Park final and Rafael Nadal a year later.
"It was tough, especially after the last match I had.
"I felt it was hard for me when I ran, so I tried to always give him a tough shot so I didn't have to run. Finally, especially in the third set, I managed to pull off some good shots and am happy about my game."
Medvedev came into the clash with a flawless 6-0 record against the 27th seed.
That included saving a match point to beat the Canadian in a titanic five-set struggle in the 2022 quarter-finals at Melbourne Park.
This time it was a one-sided affair, with Medvedev earning an early break in the opening set and rarely letting up.
Against the odds, the Canadian broke immediately in the second set, but it was temporary blip, with Medvedev getting back on level terms at 3-3.
The world number three, who has a phenomenal knack of turning defence into attack, switched up a gear to take a two-set lead after some entertaining baseline rallies.
He was unrelenting in the third set, on a mission to reach the finish line, which he did in two hours and nine minutes.