Williams began the match with heavy strapping on her knee and early on slipped, fell and jarred the damaged joint.
She screamed out in pain and looked a doubt to continue but, following a brief visit from the trainer, regained her composure to push Svitolina close in a tight first set.
She had been leading 2-0 at the time having broken Svitolina early on. Clearly troubled by the injury, she initially opted only for forehand winners in the subsequent two games, playing a part in her match statistics of 33 unforced errors.
The five-time Wimbledon champion was given a wildcard into the main draw but had struggled with injury in the lead-up.
At points, she threatened to roll back the years with an opening-day win on Centre Court but, for all the American’s aggression, Svitolina always seemed to be in the ascendancy.
The Ukrainian looked set to run away with the second set when leading 5-1 but Williams broke back and briefly threatened to change the momentum of the match before her opponent served it out.
Svitolina was the more clinical when it came to break points, converting five of nine in contrast to Williams’ stats of two from six.
Svitolina has only recently returned to the tour. She gave birth to her daughter in October and began practising in January. By May, she had won a first title since her comeback and reached the quarter-finals of the French Open.
Following the win, she said: “It’s always a a pleasure to play against Venus. It was a really special moment… against a big legend. I had to really work hard for today’s win.”