* Nadal, Federer meet for 31st time
* Djokovic, Murray breeze into last eight (Adds late matches)
CINCINNATI, Aug 15 (Reuters) - Novak Djokovic, Andy Murray, Rafa Nadal and Roger Federer all picked up third round wins at the Western and Southern Open on Thursday to set up a star-studded last eight in Cincinnati.
The ATP Tour's big four were joined in the quarter-finals by 2009 U.S. Open champion Juan Martin Del Potro of Argentina, the only other man to hoist a grand slam trophy since Marat Safin at the 2005 Australian Open.
Djokovic, Murray, Nadal, Federer and Del Potro have accounted for the last 34 grand slams and it is just the second time this year all five have reached the last eight of a tournament.
The marquee matchup on Friday will see world number five and 17-time grand slam winner Federer take on long-time rival Nadal, the world number three.
Nadal, whose grand slam resume lists 12 titles, and Federer will clash for the 31st time, adding yet another chapter to what will go down as one of the sport's all-time great rivalries.
Nadal has been in superb form coming off a win Montreal and ran his hardcourt winning streak to 12 matches with a 6-2 5-7 6-2 win over Bulgarian Grigor Dimitrov on Thursday.
"Always play against Roger is a special feeling," said Nadal, who has reached the finals in 10-of-11 events he has entered this season, claiming eight titles.
"We have a great history behind us in our confrontations, so it's another quarter-finals.
"It's a special one because you're playing against a very special player. Our matches were very special always.
"But, again, it's a quarter-finals match, not the final, so that's a big difference."
Federer, the five-time defending champion in Cincinnati, also needed three sets to see off evergreen German Tommy Haas 1-6 7-5 6-3 as he struggles to build some momentum going into the U.S. Open after missing the start of the North American hardcourt season with a sore back.
In contrast, the world's two top-ranked players, Djokovic and Murray, cruised into the quarter-finals with no-nonsense straight sets decisions.
Looking to end a run of four runner-up finishes on the Cincinnati hardcourts, world number one Djokovic needed just 50 minutes to hand Belgian qualifier David Goffin a 6-2 6-0 tennis lesson.
While Cincinnati has been a happy hunting ground for Federer, it has been a frustrating tournament for Djokovic.
But if the big Serb is the last man standing on Sunday he would become the first player to complete what the ATP Tour has dubbed the 'Career Golden Masters', winning all nine World Tour Masters events.
"I played four times (in the) finals, so it's been one of the tournaments where I've performed well actually in the last five, six years," said Djokovic. "Never managed to take final step and hopefully this year I can do so.
"I have an extra motivation and an opportunity to make history in this tournament, so I'm very inspired to play well day after day."
World number two Murray was no less ruthless, the Wimbledon champion looking right at home as he steamrolled Frenchman Julien Benneteau 6-2 6-2 in 69 minutes.
The Scot will be chasing his third Cincinnati title as he continues to prepare for the defence of his U.S. Open crown later this month at Flushing Meadows.
Djokovic will take on top-ranked American John Isner in the last eight while Murray will meet Czech sixth seed Tomas Berdych.
"You want to try and get off quickly because you need to play the next day," said Murray. "But also in 10 days' time, we're going to have to play best-of-five sets, so sometimes the long matches can kind of set you up for that well.
"But in terms of winning this event, better to get off quick because you have to play five days in a row if you want to win."
Seventh seed Del Potro battled into the quarter-finals with a 6-4 1-6 6-4 win over Spain's Feliciano Lopez and will meet Russian qualifier Dmitry Tursunov, who pulled off the upset of the day dumping world number four David Ferrer of Spain 6-2 6-4. (Editing by Mark Lamport-Stokes/Peter Rutherford)