The 19th seed has struggled for consistency this year but Roland Garros tends to bring the best out of her and so it proved again as the 2016 champion outplayed the Ukrainian on a sunny Court Philippe Chatrier.
"I feel very good in this tournament. I have always loved it since I was a little girl," Muguruza, who improved her career record at the French Open to 27-5, told reporters.
"I also love the clay. Yeah, I don't know what is about the French Open that always gives me a nice mood and my tennis develops much better."
The tall Muguruza made her intentions clear from the start, planting herself on the baseline and blazing away with her baseline power-game that Svitolina struggled to contain.
Making mincemeat of Svitolina's serve, she broke five times in the opening set, allowing her opponent only seven points on her own delivery, albeit dropping her own serve three times.
A series of service holds broke the pattern at the start of the second set before Svitolina speared an inside-out forehand winner to break and nudge 3-2 ahead.
Muguruza simply raised the intensity again, however, and won an exhausting 22-stroke rally to level at 3-3.
The two-time Grand Slam champion then powered through the last three games to book her place in the fourth round for the sixth time in eight appearances.
Muguruza made 29 unforced errors, compared to 23 winners -- a consequence of the aggressive tactics she employed. Key to her domination, however, were the 26 errors she pressurised Svitolina into making.
"This is always the idea. I have an aggressive type of game. At the beginning, we fought and I managed to hold my serve and to get the first set. I managed to dominate and play cleverly."
She will face either last year's runner-up Sloane Stephens or Polona Hercog next.