Djokovic routed Portugal's Joao Sousa in 6-0, 6-2, 6-2 fashion on the hard courts at the USTA Billie Jean King National Tennis Center.
His next foe will be Marcel Granollers of Spain, who bested the last remaining American, Tim Smyczek, by a 6-4, 4-6, 0-6, 6-3, 7-5 margin.
Meanwhile, Murray, seeking to claim back-to-back major wins following his historic victory at Wimbledon in July, downed his German opponent 7-6 (7-2), 6-2, 6-2 in 2-hour match at Arthur Ashe Stadium.
The Briton, who bested Djokovic in last year's New York finale, never lost serve in the contest.
Also posting third-round wins Sunday were fifth-seeded Czech Tomas Berdych, who sped past No. 31 Julien Benneteau of France 6-0, 6-3, 6-2, and No. 9 Swiss Stanislas Wawrinka, who overcame Marcos Baghdatis of Cyprus 6-3, 6-2, 6-7 (1-7), 7-6 (9-7).