The task may be more complicated in the next round for the 26-year-old Russian who has little taste for clay and who will face another Serb, Miomir Kecmanovic (31st), who beat Alexander Bublik on Thursday.
After winning the first two sets, Medvedev was hooked in the third by an opponent who managed a lot of winning points (39 in total).
But the Serb also committed a lot of unforced errors (68) which allowed the Russian to control the game.
With a successful break at the start of the third set and relying on an efficient serve (7 aces in total, including 3 in the third set), Medvedev was never really in danger.
He even concluded on Djere's serve by taking advantage of a double fault then a direct fault from his opponent.
"I was not confident in this third set because I only had a break in advance and on clay, a break is nothing", commented the Russian happy to have come out of a "difficult game".
Last year, he reached the quarter-finals in Paris where he passed the first round for the first time in five participations.
This year, for his sixth Roland, he arrived in the unknown after having undergone surgery to treat a "slight hernia".
Absent two months from the circuit, he returned to Geneva, just before the French Open, where he was beaten as soon as he entered the running by Richard Gasquet.
Winner of the last US Open, Medvedev was a finalist at the last two Australian Opens where he was beaten by Djokovic in 2021 and by Nadal last January.
© 2022 AFP