Colourful Kyrgios was the toast of Flushing Meadows in the lead-up to the match and delivered on all all expectations in the opening set of the third round clash on Arthur Ashe Stadium.
He dominated the first set, at one stage leading 5-0, to win 6-3 using every weapon in his arsenal.
But Kyrgios then flopped with a 2-0 lead in the second set and two break points to drop serve twice and lose the set as 32-year-old Robredo steadied the ship.
The Spainiard continued to grind it out and frustrate Kyrgios to claim the third set in a tie-break and the decisive set 6-3.
The loss leaves Casey Dellacqua as the sole Australian left in the singles draw going into the second week.
Seeded for the first time in her career at a grand slam, Dellacqua will play Italy’s world No 12 Flavia Pennetta on Monday for a place in her first slam quarter-final.
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