The second-seeded former world No. 1 star Sharapova blew past fellow Russian Vitalia Diatchenko 6-3, 6-1 on Court Chatrier, while on-fire 33-year-old Croat Mirjana Lucic-Baroni vanquished the third-seeded Romanian Halep 7-5, 6-1 on Court Lenglen.
Halep, who gave way to Sharapova in last year's French Open finale, had been 30-6 for the year before encountering the German-born Lucic-Baroni, who ended a 16-year title drought last year by capturing a championship in Quebec City.
The two-time Roland Garros titlist Sharapova also titled here in 2012. The five-time Grand Slam champion has reached at least the semifinals the last four years in Paris. In addition to her two titles, the tall Russian was the 2013 Roland Garros runner-up to Serena Williams, who also got the best of Sharapova in January's Aussie final.
Next up for Sharapova will be 26th-seeded Aussie Samantha Stosur, who whipped France's Amandine Hesse 6-2, 6-0. Stosur is a former U.S. Open champion and was the French Open runner-up back in 2010.
In other action involving seeds, No. 13 Czech Lucie Safarova drilled Japan's Kurumi Nara 6-2, 6-0, No. 20 German Sabine Lisicki, a former Wimbledon runner-up, got past Russian Daria Gavrilova, who retired after dropping the first set 6-1, and No. 29 French favorite Alize Cornet handled Romanian Alexandra Dulgheru 6-2, 7-5.