PARIS, June 1, 2018 (News Wires) - American 13th seed Madison Keys overcame a second-set wobble to beat Japan's Naomi Osaka 6-1 7-6(7) and reach the last 16 of the French Open for the second time on Friday. A match between two of the biggest hitters on the WTA Tour failed to really catch fire on a cool and half-empty Suzanne Lenglen Court with Keys helped on her way to the first set by a succession of wild errors from Osaka. Keys broke for a 3-1 lead in the second set and looked to be closing in on a straightforward victory when 21st seed Osaka suddenly found her range and levelled the set. Osaka's mini-revival looked to have fizzled out when she dropped serve with a double-fault at 4-4. Keys squandered a match point in the next game, however, and the 23-year-old US Open runner-up looked increasingly tight as the set moved into a tiebreaker. Osaka led 4-1 but Keys dragged it back to 4-4 with a searing backhand pass but faced a set point at 5-6 and needed some superb defence to fend off the fired-up Japanese. Keys saved another set point at 6-7, this time with a booming first serve. She then wrong-footed Osaka to bring up a second match point and was relieved as her opponent coughed up another double-fault to end the contest. She will face either fourth seed Elina Svitolina of Ukraine or Romanian Mihaela Buzarnescu next. Keys is one of three Americans to reach the third round with Sloane Stephens, who beat her in the Flushing Meadows final last year, and three-time champion Serena Williams also in the hunt. Serena Williams battled back from a set and break down to defeat Australia's Ashleigh Barty 3-6, 6-3, 6-4 to reach the French Open third round on Thursday. The three-time champion and former world No 1, dressed again in her all-black catsuit, is playing her first Slam since winning the 2017 Australian Open while two months pregnant. The 36-year-old, seeking a 24th Grand Slam title, will face Germany's Julia Goerges for a place in the last 16. If she gets past the third round, Williams could face old rival Maria Sharapova for a place in the quarterfinals. "It's just incredible," said Williams. "I am so happy to be back here. I lost the first set and thought I must try harder, I must try harder and then Serena came out. "I will be back tomorrow to play doubles with Venus. I don't mind playing singles and doubles -- I will fight my heart out." Ten-time champion Rafael Nadal breezed into the third round and a clash against childhood friend Richard Gasquet. Top seed and world No 1 Nadal, chasing an 11th title, swept past Argentinian Guido Pella 6-2, 6-1, 6-1, showing no signs of the brief struggles he faced in the first round against lucky loser Simone Bolelli. The 31-year-old will next face home favourite, and his old junior rival Gasquet, whom he has beaten 15 times from as many meetings in professional tennis. "Richard is a very good friend. We've known each other since we were 11 or 12 years old so it will be very special to play again against him," said the champion.