By Martyn Herman
PARIS (Reuters) - Roger Federer and Maria Sharapova made smooth progress into the last 16 of the French Open and Alize Cornet celebrated as if she had won the title as she led a home charge at Roland Garros on Friday.
Reaching the fourth round of grand slam tournaments is bread and butter for Federer and Sharapova and for them the real business now begins.
Men's second seed Federer, bidding for a second French Open title and 18th major overall, looked as cool as the dull Paris weather as he beat Bosnia's Damir Dzumhur 6-4 6-3 6-2.
Defending women's champion Sharapova's third round clash against former runner-up Samantha Stosur looked potentially dangerous for the Russian but she was dominant throughout against the 26th seeded Australian whose challenge fizzled out.
"Just getting the job done," 28-year-old Sharapova, still suffering from a cold, told reporters after the 6-3 6-4 win.
"I was just really happy to win this one."
If Sharapova's mood appeared a little flat, French number one Cornet's was ecstatic as she reached the fourth round for the first time, coming from a set down to beat Croatian former teen sensation Mirjana Lucic-Baroni 4-6 6-3 7-5.
When Lucic-Baroni, now 33, blasted a return long on match point, the Chatrier Court crowd erupted and Cornet collapsed joyfully on to her back behind the baseline -- a celebration usually reserved for finals weekend.
"Sometimes I would jump, sometimes I would yell," 29th seed Cornet, making her 11th main draw appearance at the French Open, told reporters. "It's not something I think about beforehand.
"But after this two-and-a-half-hour fight, I felt so relieved that I fell on the ground. A bit like Rafa."
Her next challenge will be Ukraine's Elina Svitolina, the 19th seed.
France's last women's champion here was Mary Pierce in 2000 while Yannick Noah's 1983 triumph is the last time a Frenchman got his hands on La Coupe des Mousquetaires.
Few expect that wait to end this year but there is hope.
Cornet only has Kristina Mladenovic to share the burden but the men advanced to the third round en masse with Richard Gasquet making it seven, only one short of the professional era record, when he returned to court on Friday to complete a second round win over Argentina's Carlos Berlocq.
After their match was tied at two sets all overnight, Gasquet needed 32 minutes to win the decider 6-1.
French number one Gilles Simon was the first home player through to the last 16 when he beat compatriot Nicolas Mahut 6-2 6-7(6) 6-7(6) 6-3 6-1.
Jo-Wilfried Tsonga was up against Spain's Pablo Andujar trying to reach the last 16 for a fourth year running while crowd-pleaser Gael Monfils was playing Uruguay's Pablo Cuevas.
Benoit Paire's run was ended by Czech fourth seed Tomas Berdych 6-1 6-7(5) 6-3 6-4.
Former champion Ana Ivanovic wasted little time reaching the last 16, hitting top form after two close three-setters to thrash Croatian teenager Donna Vekic 6-0 6-3.
The Serb has not been beyond the fourth round since she won the title in 2008 and will have to beat ninth seed Ekaterina Makarova if she is to improve on that record.
Federer was joined in the fourth round by fellow Swiss Stanislas Wawrinka who saw off Steve Johnson 6-4 6-3 6-2 to leave Jack Sock as the sole remaining American man.
(Reporting by Martyn Herman; Editing by Mark Meadows)