Garcia, seeded five, has a game suited to grass and used her speed and agility at the net as well as powerful returns to grind down her 21-year-old opponent.
Garcia, 29, who has twice reached the fourth round at Wimbledon, suffered a brief wobble at the start of the second set, spraying unforced errors around the court and Volynets took advantage, breaking serve twice for a 3-0 lead.
The Californian, whose only previous Wimbledon main draw appearance in 2021 ended in first-round defeat, could not cope when Garcia put her game back together.
"I had to have a reaction and I was able to come back quickly," Garcia said in an on-court interview.
When play resumed Garcia did not hang about, winning the fifth game in a row when Volynets served a double fault then serving for the match.
Persons:
Caroline Garcia, Katie Volynets, Toby Melville LONDON, drizzle, Garcia, Volynets, volleying, Clare Lovell, Ed Osmond
Organizations:
Lawn Tennis, Croquet Club, U.S, REUTERS, Wimbledon, Thomson
Locations:
London, Britain