Coming off his upset second round win over the sixth-seed Juan Martin Del Potro, Hewitt was able to back that up on Sunday with a 6-3, 7-6 (5), 3-6, 6-1 victory against Evgeny Donskoy.
Other winners in Sunday's third round action included the defending champion Murray, world No. 1 Djokovic, fifth-seed Berdych, ninth-seed Wawrinka, the 21st-seeded Russian Mikhail Youzhny and Uzbekistan veteran Denis Istomin.
Notable losers were 35-year-old German 12th-seed Tommy Haas with Italian Andreas Seppi and Marcos Baghdatis all bowing out in the third round in the final Grand Slam of 2013 at Flushing Meadows.
While Hewitt was without doubt facing a lesser opponent in the world No. 84 Russian Donskoy after taking out former US Open champion Del Potro in the second round, it was always going to be a matter of if the 32-year-old Australian two-time major win could back up from that physical hit out.
He certainly started brightly breaking the Russian 23-year-old to love in the first game of the match and then racing to a 2-0 lead before winning the first set 6-3.
However, Hewitt perhaps tired or took his foot off the gas a little after that with Donskoy feeling more at ease on the big stage to push the second set to a tie-break, and then win the third but the former world No. 1 was too good in the end winning 6-3, 7-6 (5), 3-6, 6-1.
It is the first time that Hewitt has made the fourth round at the US Open since he made the quarter finals in 2006, and at that time he had reached at least the quarters in seven straight years at Flushing Meadows while winning the title in 2001 and making the final in 2004.
However, this is now his best performance in New York in seven years and it's also his first Grand Slam fourth round appearance of any description since the Australian Open of 2012, and it's just his second time into the round of 16 at a major since the 2009 Wimbledon quarter-final.
Hewitt now can look forward to a fourth round match-up with Russia's Youzhny who advanced by knocking out German veteran Haas in the third round, 6-3, 6-2, 2-6, 6-3.
The defending US Open champion Murray had every reason to expect a tough battle up against German Florian Mayer in the third round, but after a first set tie-break he did well in the hot and humid conditions to come away with the 7-6 (2), 6-2, 6-2 victory.
The world No. 3 will now face Uzbekistan's world No. 66 and 26-year-old Istomin who advanced to the fourth round with somewhat of an upset five-set win over 20th-seeded Italian Seppi, 6-3, 6-4, 2-6, 3-6, 6-1.
World No. 1 Djokovic needs to either win the US Open himself or not allow Rafael Nadal to do so to keep top spot in the rankings, and he had no trouble advancing to the fourth round with a comfortable 6-0, 6-2, 6-2 win over Portugal's Joao Sousa.
The Serb will now take on Spain's Marcel Granollers in the fourth round after the world No. 46 needed five sets to beat American, Tim Smyczek 6-4, 4-6, 0-6, 6-3, 7-5.
Remarkably with Smyczek's exit it now means that there is no American man left in the main draw of their home Grand Slam heading into the fourth round.
Even more amazingly, no American male player has reached the fourth round of any Grand Slam this year with John Isner, Sam Querrey, Jack Sock and Ryan Harris the most likely candidates, but they haven’t been able to.
Former world No. 7 Mardy Fish continues to be sidelined with health issues and his career is in serious jeopardy as well following Andy Roddick and James Blake having now retired in the past 12 months.
It's a far cry from little more than a decade ago when Fish, Roddick and Blake were coming through on the back of the dominance of Pete Sampras, Andre Agassi, Jim Courier and Michael Chang, and before them Jimmy Connors and John McEnroe.
Perhaps the most anticipated and hardest to predict match on Day 7 was on Louis Armstrong Stadium before former world No. 8 and Australian Open finalists Baghdatis, and current ninth-seed Wawrinka.
The Swiss cruised through the first two sets, but he tired in the heat and humidity with the Cypriot taking his game up a level to claim the third set in a tie-break. However, Wawrinka steadied to claim the fourth set tie-break to win the match, 6-3, 6-2, 6-7 (1), 7-6 (7).
Things won't get any easier for Wawrinka, though, with his fourth round opponent to be Czech No. 5 seed Berdych.
The former Wimbledon finalist thumped Frenchman Julien Benneteau 6-0, 6-3, 6-2 on Sunday as the 27-year-old continues to loom as a legitimate title contender at the US Open.
There are four men's fourth round matches to take place now on Monday and each of them is set to be a fascinating battle.
Roger Federer and Rafael Nadal might appear on a collision course in the quarter finals but first Federer has to get by Spanish veteran Tommy Robredo, and Nadal has to beat in-form German 22nd-seed Philipp Kohlschreiber. Both those matches are back-to-back on Arthur Ashe Stadium.
French eighth-seed Richard Gasquet takes on Canadian No. 10 seed Milos Raonic on Louis Armstrong Stadium and then on the Grandstand, world No. 4 David Ferrer takes on Serb 18th-seed Janko Tipsarevic.