The world number one, eyeing a 20th grand slam singles title, raced into a 3-0 lead but was given a decent workout after that by a player she beat 6-0 6-0 in their only previous meeting three years ago at the U.S. Open.
Hlavackova broke the mighty Williams serve in the fifth game, but the first set was otherwise mostly one way traffic as the American unloaded some heavy groundstrokes under grey skies on a cool day on court Philippe Chatrier.
In the second, the veteran American played with clinical economy, winning the only break point she got and saving both of those she faced.
Williams, who has already bagged the Australian Open crown this year, last won the title in Paris in 2013 and has reached the quarter-finals or better eight times, but she crashed out in round two last year to Spaniard Garbine Muguruza.
Doing worse in an event than a year ago costs players world ranking points.
"I felt good, defended my points, so I'm excited about that," she joked. "That's always exciting."
Arch rival and defending champion Maria Sharapova, also looking for a third French Open title, awaits at the other end of the draw in a potential final.
Serena's older sister Venus went out on Monday to fellow American Sloane Stephens.
(Reporting by Andrew Callus; editing by Ken Ferris)
Share
