The world number one, who had not played since early March when he reached the final in Dubai after being forced to skip Indian Wells and Miami because of his COVID unvaccinated status, struggled to find his range on the Monte Carlo clay before prevailing on a sunlit centre court.
Gakhov went for his shots and claimed the first service break to lead 4-3, only for the Serbian to break right back and take the opening set by winning the tiebreak 7-5.
Djokovic was then business like in the second set, leaving no chance of a comeback for his opponent, who suddenly felt the court was too big for him.
The double French Open champion, who suffered an opening-round exit here last year, will next face Lorenzo Musetti (21) or the 16th seed's Italian compatriot Luca Nardi (19).
German Alexander Zverev (25), who suffered a serious ankle injury in his French Open semi-final clash against Rafael Nadal (36), was back on the claycourts with a 3-6 6-2 6-4 first-round win against Kazakhstan's Alexander Bublik (25).
Spain's Nadal, who triumphed a record 11 times at the Monte Carlo Country Club, is absent after failing to recover from a hip injury that has kept him away from the courts since the Australian Open.
His compatriot Carlos Alcaraz (19) is also missing the tournament with hand and back problems.
