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 buildup to the U.S. Open later this month after falling to Frenchman Jo-Wilfried Tsonga in the third round 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 U.S. 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.
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.
“When I finish my career and when I will be sitting at home and talking with friends, I will remember days like this,” Robredo said.
The win marked his second win over a world number one for the 32-year-old Robredo, who also beat Lleyton Hewitt in 2003.
Former world number one Roger Federer avoided tasting an upset of his own as he held off Frenchman Gael Monfils 6-4 4-6 6-3.
A five-time winner at Cincinnati, Federer will now face Andy Murray in the quarter-finals after the Briton had to overcome a stern test against American John Isner.
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.
Eighth seed Murray, twice a Cincinnati champion, also need three sets and two and a half hours to tame Isner 6-7(3) 6-4 7-6(2).
The 11th seeded Isner, a Cincinnati finalist a year ago, blasted 21 aces past his Scottish opponent but could not manage a break the entire match.
“It’s a very important match for me to win,” said Murray. “I had lost a few close matches, matches like that over the last few months. So, yeah, it was important for me to come through.
“It was a really, you know, good atmosphere to get ready for the rest of the tournament, but also the U.S. Open, as well.”
In the women’s draw, the world number one Serena Williams cruised into the quarter-finals with a 6-2 6-2 win against Flavia Pennetta.
Williams served eight aces and broke the Italian five times in their hour-long match.
“I have a lot more confidence,” Williams said. “I feel more relaxed. Overall feel a lot better. I’m playing a lot better.
French Open champion Maria Sharapova also advanced with a victory against Anastasia Pavlyuchenkova 6-4 7-6 (2).
Sharapova’s win sets up a match against Simona Halep, who she beat in the Roland Garros final after the Romanian beat Lucie Safarova 6-4 7-5 to advance.
Caroline Wozniacki and Jelena Jankovic also advanced with straight set victories. (Reuters)