Hewitt had won through to his first fourth round at the US Open since 2006 and his first at any Grand Slam since the 2012 Australian Open with two solid wins over Brian Baker and Evgeny Donskoy, and a brilliant upset over No. 6 seed Juan Martin Del Potro.
The former world No. 1 32-year-old started slowly against the 21st-seeded Youzhny losing the first set in no time after falling 3-0 down, but Hewitt worked his way into the contest from there and the Russian grew increasingly frustrated with proceedings.
Hewitt broke Youzhny's serve twice in the second set to level things up before the third went to a tie-break, but the Australian dominated that seven points to three.
He then looked on track for another memorable New York victory going up two breaks in the fourth set to lead 4-1, however the Russian dug deep to find something and break back, and then go up with an advantage of another break to force the match into a deciding fifth set.
The fifth set proved to be a gruelling 62-minute battle but it was Hewitt who opened up what appeared to a match-winning advantage at 5-2 with two breaks of serve even after dropping his opening service game.
However, Youzhny broke Hewitt's last two service games to claim the match 6-3, 3-6, 6-7 (3), 6-4, 7-5 in just under four hours.
In the end, even though Hewitt hit more winners (55 to 47) and won more total points (146 to 145) in the match, it was the Russian who prevailed in the five-set thriller to advance to the quarter finals and book in a match-up with world No. 1 Novak Djokovic.
Djokovic, who needs to either win at Flushing Meadows or make sure Rafael Nadal doesn’t to keep his hold on top spot in the rankings, had an incredibly easy time of it in his fourth round match thumping Spaniard Marcel Granollers 6-3, 6-0, 6-0 in just an hour and 19 minutes.
While it is a daunting ask for Youzhny to beat Djokovic to advance to the semi finals, he has actually beaten the Serb three times in their eight meetings.
Their meeting in this year's quarter finals at the US Open will be the first time they have played in New York, and only the second time they've ever meet in a Grand Slam with Djokovic winning at the 2006 Wimbledon in four sets.
Defending US Open champion Andy Murray was last up on Arthur Ashe Stadium on Tuesday and he also had a hard time of it against Uzbekistan's Denis Istomin.
Istomin, ranked 65 in the world but who has been as high as 33, won the opening set against the Brit in a tie-break and despite a tight third and fourth sets, Murray was able to get over the line 6-7 (5), 6-1, 6-4, 6-4.
Little separated both players all night in a terrific struggle with Murray serving five aces to Istomin's four, Murray hitting 38 winners to 33 from Istomin and Murray 35 unforced errors to 36 from Istomin.
However, Murray just got on top in terms of winning 77 per cent of his first serves and in forcing 15 break points of which he was able to capitalise on six in the end.
Murray will now take on Swiss No. 9 seed Stanislas Wawrinka who scored a terrific fourth round victory over fifth-seeded Czech Tomas Berdych on Tuesday.
Berdych won the first set but Wawrinka worked his way on top from there to come away with the 3-6, 6-1, 7-6 (6), 6-2 victory.
Wawrinka is into just the fourth quarter-final of his Grand Slam career having previously made that mark at this year's French Open, the 2011 Australian Open and 2010 US Open.
However, he has never made it to a semi-final at a major and now will have to beat the defending champion Murray.
Wawrinka, though, has a respectable head-to-head record against Murray having won five of their 13 meetings including their last clash earlier this year at the Monte Carlo Masters where he won 6-1, 6-2.
The Swiss 28-year-old did win the pair's last Grand Slam meeting at the US Open in the third round in 2010 when he won in four sets. Murray beat Wawrinka in three sets in the round of 16 at the 2008 US Open though.
The men's quarter finals get underway on Wednesday with Richard Gasquet and David Ferrer first-up on Arthur Ashe Stadium before the clash of the Spaniards between Tommy Robredo and Rafael Nadal closes out proceedings in the evening session.