Hewitt, 32, the champion at Flushing Meadows in 2001, recovered from a lapse in the second set to defeat Russia's Evgeny Donskoy 6-3 7-6(5) 3-6 6-1 in two hours and 55 minutes on the Grandstand court.
Hewitt will face either Germany's 12th seed Tommy Haas or 21st-seeded Russian Mikhail Youzhny for a berth in his first quarter-final at a major since Wimbledon in 2009.
Riding strong crowd support at Flushing Meadows after recovering from five surgeries in recent years, Hewitt won 24 of 31 points at the net in an aggressive display.
"It's always great to come back to where it all started for me," he said. "The atmosphere in New York suits my personality. It's a lot of fun here, always."