Spain's Robredo, seeded 16th in the US Open tune-up, sent top-seeded Djokovic packing 7-6 (8/6), 7-5, the defeat coming a week after the world number one Serb was beaten in the third round at Toronto.
The Wimbledon champion now goes into the US Open, the final Grand Slam of the year which starts on August 25, well short of matches and confidence.
Second-seeded Federer, a five-time Cincinnati champion, held off Monfils 6-4, 4-6, 6-3 on Thursday.
He booked a tough quarter-final against eighth-seeded Scot Andy Murray, who battled more than two hours against the huge serve of John Isner, finally dispatching the American 6-7 (3/7), 6-4, 7-6 (7/2).
But Federer quickly recovered his poise, clinching the match with a service winner after breaking Monfils in the penultimate game.
"I'm just happy the way I'm playing right now," Federer said. "It was much better than the last couple of matches.
"I was hitting good forehands, not making so many mistakes, returning better," he added. "So there was a lot of positives out in the match. Sometimes frustration, but sometimes that's what Gael does to you."
========================
Djokovic, who was married last month and is soon to become a father, said it wasn't a question of the new elements in his life weighing on his tennis.
"I just lost the match," he said. "It was bad. Many, many things are not clicking these two weeks on hard courts. 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 the US Open. I just don't feel comfortable. That's it.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
