* Shaky Williams recovers to beat unheralded Friedsam
* Fifth seed Wozniacki knocked out by Germany's Goerges
* Nadal, Djokovic and Murray all reach third round (Adds quotes)
By Martyn Herman
PARIS, May 28 (Reuters) - The pre-tournament shortlist of favourites for the French Open women's crown continues to shrink and for a while it looked as though the top name, Serena Williams, would also vanish on Thursday.
Shortly after former world number one Caroline Wozniacki was knocked out by Julia Goerges, meaning the third, fifth and sixth seeds had all gone before round three, Williams, 33, faced unheralded 21-year-old German Anna-Lena Friedsam.
It looked like a mismatch but 105th-ranked Friedsam gave the 19-times grand slam champion a torrid time on Court Suzanne Lenglen, taking the first set off the American before a nervy Williams recovered to scrape into the third round 5-7 6-3 6-3.
Twice former champion Williams has suffered at the French before, namely last year when she was beaten by Spain's Garbine Muguruza at the same stage and more memorably in 2012 when France's Virginie Razzano knocked her out in round one.
With the American's trademark groundstrokes regularly sailing over the baseline and even her fearsome serve deserting her in the first set -- she was broken three times -- another blot on her incredible grand slam record looked possible.
Even when she led 4-2 in the second set, Williams looked shaky, going 0-40 down and dropping serve, but once she got level and broke Friedsam's serve at the start of the decider she finally began to relax.
"A win is a win, and as long as you live to survive the next day, you can always improve," Williams said. "I know my level is literally a hundred times better than I played today.
"I think I take more solace in the fact I can play better as opposed to the fact that that's the best I could play -- then I would be in trouble."
She will have to sharpen up considerably though against former world number one Victoria Azarenka in the next round.
Denmark's Wozniacki joined the exodus of women's seeds, which includes Romanian third seed Simona Halep, last year's runner-up, and number six Eugenie Bouchard of Canada, by losing 6-4 7-6(4) to Goerges on a blustery Phillipe Chatrier court.
Fourth-seeded Czech Petra Kvitova survived her own trial, however, coming back to beat Spain's Silvia Soler-Espinosa 6-7(4) 6-4 6-2 despite 54 unforced errors.
In contrast to the shocks in the women's draw, the men's favourites have been largely untroubled and that continued on Thursday as defending champion Rafa Nadal, top seed Novak Djokovic and in-form Andy Murray all reached the third round.
All eyes have been on Nadal as the Spaniard battles to rediscover his mojo in time for a bid for a record-extending 10th French Open title, but their were few weaknesses on show as he beat compatriot Nicolas Almagro with relative ease.
Nadal took his stunning Roland Garros record to 68-1 with a routine 6-4 6-3 6-1 victory -- his fourth without dropping a set against Almagro on the Paris clay.
Djokovic needed an injury timeout when slipping and stretching his groin in a straight sets win over Luxembourg's Gilles Muller, although he looked untroubled when shaking hands with watching Swedish soccer great Zlatan Ibrahimovic.
Third seed Murray was given a fight by Portugal's Joao Sousa but came through 6-2 4-6 6-4 6-1 to set up an eye-catching clash against Australian trailblazer Nick Kyrgios.
Some of the biggest cheers came elsewhere at the tournament.
On Court One, nicknamed the Bull Ring, former women's champions Francesca Schiavone and Svetlana Kuznetsova battled toe-to-toe for three hours and 50 minutes before Italian Schiavone prevailed 6-7(11) 7-5 10-8.
Russian Kuznetsova served for the match four times in the third set and had one match point which Schiavone, 34, saved with a magical backhand before the Italian summoned one last effort to edge ahead and clinch a memorable victory.
On Court Seven, fans crammed in to watch Australian teenager Thanasi Kokkinakis beat his country's former trailblazer Bernard Tomic 3-6 3-6 6-3 6-4 8-6. (Reporting by Martyn Herman, editing by Justin Palmer)