Rafael Nadal trailed in the second set before overcoming No. 5 seed Cameron Norrie of Great Britain.
Barty survived a first-round scare at the US Open on Monday
Three fancied players did succumb on a cheerless day.
French Open champion Stan Wawrinka warmed up for the defence of his title at Roland Garros with a 6-4, 7-6(11) victory over Marin Cilic to win the Geneva Open title on Saturday.
A 1,000km 10-hour roadtrip dash to Paris, squeezed into a small hire car alongside his 88-year-old grandmother, ended in Grand Slam joy for Marco Trungelliti at Roland Garros on Monday -- and a guaranteed 79,000 euros ($92,000) payday.
IMAGES from matches played on Day 4 of the French Open at Roland Garros on Wednesday