Hewitt moved into the final 16 for the seventh year in a row after ousting Monfils 6-3, 7-6 (9), 6-4 in just over two hours.
The Australian had the match under control after winning a thrilling second-set tiebreaker, in which he saved three set points after squandering two of his own.
The 2002 champion was broken after moving to a 4-1 lead in the third but Monfils could not continue his run and double-faulted to end the match.
Hewitt, one of only three Wimbledon men's champions in the draw, has not beaten the third-seeded Djokovic since the third round of the U.S. Open in 2006 and has lost their past three matches.
The 29-year-old is enjoying a resurgence after being sidelined for two months to recover from hip surgery earlier this year.
He defeated Roger Federer last week at Halle to capture his first ATP title since winning in Houston on clay in April 2009.