The Belarusian dominated her opponent from the start and although she faced some brief resistance in the second set, she easily set up a meeting with 16th seed Amanda Anisimova of the United States.
"I am super happy with the win, Olga is a fighter and I knew it would be a fight. She played like a top 10 player; pretty soon she will be in the top 10," said Sabalenka.
Sabalenka started in ruthless fashion, racing to a 5-0 lead but Danilovic avoided the bagel by winning the sixth game on serve, going on to pull a break back.
The resurgence was short-lived, however, as Sabalenka wrapped up the opening set with another break of serve.
Danilovic put up a decent fight in the second set but there was no comeback on the cards as Sabalenka broke for 5-3.
The three-time Grand Slam champion wrapped it up with an unreturnable serve on a half-empty Court Philippe Chatrier - a common occurrence on early matches at the French Open.
