* Nadal sees off Mayer in three sets
* Bad light halts Murray v Kohlschreiber in fifth set
* Halep glides through to fourth round
* Former champion Ivanovic out
PARIS, May 31 (Reuters) - Rafa Nadal once again showed he is the man to beat at the French Open after putting down a brief rebellion from Argentine Leonardo Mayer to win 6-2 7-5 6-2 and reach the fourth round despite a sore back on Saturday.
Mayer went for his shots in a tense second set and broke the world No.1 back for 4-4, only for the Spaniard to regain control in commanding fashion.
"It is for me very emotional thing when I am on (court Philippe) Chatrier, a lot of memories come to my mind," said Nadal, who made only 10 unforced errors with just two coming in a masterful opening set.
One moment that may live long in the memory occurred in the second set when the defending champion recovered after being wrongfooted by Mayer to pull off a perfect backhand lob to break decisively for a 6-5 lead.
He followed up with a game to love, sealing the set with a jaw-dropping forehand passing shot before steaming through the third and ending the contest with a service winner.
In the aftermath, Nadal revealed he was suffering with back pains, but would not be drawn on the details.
"Well, I'd rather not talk about my back. I'll play as best as I can. I'll put up a good fight to try and win," he said.
Nadal next faces Serbian Dusan Lajovic, who beat American Jack Sock 6-4 7-5 6-3 and, like the Spaniard, has yet to drop a set.
Should he prevail, he could face compatriot David Ferrer in the quarter-final, the man he beat to claim last year's title and one of three men to have beaten him on the red dust this season.
A possible semi-final encounter against Andy Murray was hanging in the balance, however, after the Wimbledon champion's encounter with 28th seed Philipp Kohlschreiber was suspended due to bad light in the fifth set.
Seventh seed Murray and German Kohlschreiber were locked together at 3-6 6-3 6-3 4-6 7-7 when play was interrupted at 2139 local time, after the Briton had blown a 4-2 lead in the fourth set.
The fifth-seeded Ferrer continued his stroll through the draw with a 6-2 7-6(2) 6-3 win against Italian Andreas Seppi.
He next faces South African 19th seed Kevin Anderson who went through after Croatia's Ivo Karlovic retired because of a sore back.
While Nadal and Ferrer produced flawless performances, Italian 14th seed Fabio Fognini and Frenchman Gael Monfils made 137 unforced errors between them - in 278 points - during a poor quality third-round clash.
The local favourite won 5-7 6-2 6-4 0-6 6-2 and will now meet Spain's Guillermo Garcia Lopez.
The match between Frenchman Richard Gasquet, the 12th seed, and Spanish 24th seed Fernando Verdasco was interrupted because of bad light with Verdasco leading 6-3 6-2 2-2.
Earlier, Simona Halep had too many tricks up her sleeve for Spaniard Maria-Teresa Torro-Flor as the fourth seed glided into the fourth round with a 6-3 6-0 win.
The wily Romanian, the highest seed left in the draw after Serena Williams, Li Na and Agnieszka Radwanska were knocked out early, found perfect angles and defended superbly to counter Torro-Flor's powerful forehand in Paris.
"It's not a surprise because I'm more confident now in myself, and I feel the ball really good here at the French Open," said Halep, who has won more titles in the last 12 months than any other woman except Williams.
Halep, who has dropped only 11 games in three straight-set wins, will next meet American 15th seed Sloane Stephens for a place in the quarter-finals.
Stephens was in less devastating form than in her first two matches but she was still too strong for Ekaterina Makarova in a 6-3 6-4 win over the Russian left-hander.
The American has shown her consistency on the big stage by reaching the fourth round at six successive grand slam events, the only active woman to do so.
Roland Garros has not been a happy hunting ground for Ana Ivanovic since she won the title in 2008 and the popular Serbian failed to break that jinx on Saturday as she lost 6-3 6-3 to Czech Lucie Safarova.
Safarova will face another champion in 2009 winner Svetlana Kuznetsova after the Russian 27th seed beat Czech fifth seed Petra Kvitova 6-7(3) 6-1 9-7 in three hours 13 minutes on Philippe Chatrier court.
Kvitova took two medical timeouts and came back from the first with a heavily strapped right thigh, but it did not seem to hamper her as she peppered the court with winners.
But her 65 unforced errors eventually cost her as she bowed out on the third match point.
Italian 10th seed Sara Errani, runner-up in 2012, won 20 points in succession during her 6-0 6-1 demolition of Israel's Julia Glushko. She set up a meeting with Serbian sixth seed Jelena Jankovic who demolished Romanian Sorana Cirstea 6-1 6-2. (Reporting by Julien Pretot; Editing by Pritha Sarkar and Toby Davis)