Tunisian Jabeur, still seeking her first major singles title after three runner-up finishes, was ruthless in dispatching American wildcard Sachia Vickery 6-3 6-2.
The 29-year-old reached the quarter-finals at Roland Garros last year and made the Wimbledon final a month later, losing to Vondrousova. Jabeur had suffered previous finals defeats at Wimbledon and the US Open in 2022.
After her victory on Monday, she spoke of being a role model in the Arab world and how she tries to keep composed in between and during matches.
Jabeur said she used “a lot of meditation, a lot of breathing exercises” and added: “I chose this path intentionally, and I try to give the best image possible of myself to be a leading figure for the young people.”
Vondrousova completed an emphatic 6-1 6-3 victory over Spain’s Rebeka Masarova in the morning before the rain arrived.
US Open champion Gauff only needed 52 minutes to complete a convincing 6-1 6-1 victory over 21-year-old Russian qualifier Julia Avdeeva, the world number 208.
Twelfth seed Jasmine Paolini of Italy beat Australia’s Daria Saville 6-3 6-4 and Russian 17th seed Liudmila Samsonova thrashed Poland’s Magda Linette 6-1 6-1.
Britain’s Harriet Dart is among those still to play on Monday, with British number one Katie Boulter in action on Tuesday when she faces former world number two Paula Badosa of Spain.