For the 16th seeded Robredo the victory was his first over Djokovic since their first meeting in 2005, the Serb sweeping their next six meetings.
The loss brought a temporary halt to Djokovic's bid to become the first player to win all nine ATP World Tour Masters events during his career.
It was also another setback in the Serb's build-up to US Open later this month after falling to Frenchman Jo-Wilfried Tsonga in the third round of the Rogers Cup last week in Toronto.
"Many, many, many things are not clicking these two weeks on hard courts," said Djokovic. "It's unfortunate but it's more than obvious I'm not playing even close to what I'm supposed to play.
"I have to keep on working and trying to get better for US Open.
"I just don't feel comfortable.
"It's disappointing that I'm finishing Cincinnati again with a tough loss but it's sport. I didn't play well in Toronto; didn't play well here.
"Hopefully it's going to be different in New York."
While Djokovic has hoisted the Canada trophy three times he has not felt the same comfort level on the Ohio hard courts, reaching the finals four times in 10 visits to Cincinnati and losing all four.
Certainly the Serb appeared out of his normal rhythm, particularly in the second set when he failed to gain even a single break chance.
Robredo managed three break opportunities and only needed to capitalise on one to secure the upset.
"I thought his forehand was really good," said Djokovic. "Served very efficiently, especially second serve. He was playing great, no question about it."
Andy Murray overcame going a set down to beat John Isner 6-7 6-4 7-6 to progress to the quarter-finals of the Cincinnati …
Eighth seed Murray, twice a Cincinnati champion, came back from a set down to beat Isner 6-7(3) 6-4 7-6(2) and progress to the quarters.
American Isner, a Cincinnati finalist a year ago, prevailed in a first set tie-breaker but Murray rallied to secure the second set courtesy of the only break of serve of the whole match.
Murray had to stave off two match points in the decider before taking the tie-breaker 7-2 to move into the quarters.
Murray will now face Roger Federer, a five-times winner at Cincinnati, in the quarters after the former world number one also avoided tasting an upset as he held off Frenchman Gael Monfils 6-4 4-6 6-3.
"It was a big win for me because he plays very well here," Murray told the BBC.
"Returning his serve in these conditions is very challenging and I did well to fight back.
"I felt I played a very good match. When challenged at the end I felt I responded well."
Third seeded Swiss Stan Wawrinka rallied past 14th seed Marin Cilic 3-6 6-0 6-1 to book his place in the last eight.
The Australian Open champion got off to a sluggish start losing the opening set to the big-hitting Croatian but then could do little wrong, blazing through the next two sets dropping just a single game along the way.
Unable to register even a single break chance in the first, Wawrinka broke Cilic five times over the next two sets to seal the win.
Cincinnati Masters results
6-David Ferrer (Spain) beat Mikhail Youzhny (Russia) 7-5 6-0
2-Roger Federer (Switzerland) beat Gael Monfils (France) 6-4 4-6 6-3
5-Milos Raonic (Canada) beat Steve Johnson (U.S.) 6-7(7) 6-3 7-6(4)
16-Tommy Robredo (Spain) beat 1-Novak Djokovic (Serbia) 7-6(6) 7-5
8-Andy Murray (Britain) beat 11-John Isner (U.S.) 6-7(3) 6-4 7-6(2)
15-Fabio Fognini (Italy) beat Lu Yen-Hsun (Taiwan) 3-6 6-3 6-3
3-Stanislas Wawrinka (Switzerland) beat 14-Marin Cilic (Croatia) 3-6 6-0 6-1
Julien Benneteau (France) beat Jerzy Janowicz (Poland) 7-5 6-1
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