Djokovic, seeded second in New York, breezed past No. 31 Julien Benneteau of France 6-3, 6-2, 6-2, reaching the fourth round at Flushing Meadows for the sixth consecutive year.
The Serbian superstar will next face 18th-seeded Swiss Stanislas Wawrinka, who moved on with a 6-4, 6-4, 6-2 win over 14th-seeded Ukrainian Alexandr Dolgopolov.
Roddick -- who won the U.S. Open in 2003 and has announced he will retire after this year's event -- kept his career going with a 7-5, 7-6 (7-1), 4-6, 6-4 decision over Italian Fabio Fognini.
He now goes on to oppose Argentina's Juan Martin del Potro, who dispatched countryman Leonardo Mayer 6-3, 7-5, 7-6 (11-9) to reach the Round of 16.
Interpol investigating stolen passports on missing flight
Scarlett Johansson steps out with fiance after pregnancy reveal