Former world number one Hewitt faced a momentous task having never beaten Federer in their 15 previous matches.
BBC: Roger Federer eases into Australian Open quarter-finals
Sixth seed Nikolay Davydenko, who has beaten Federer in their past two meetings, kept alive the possibility of another encounter in the quarterfinals by beating German qualifier Dieter Kindlmann 6-1 6-0 6-3.
Their cause has been led by a rare group of all-time players in their prime: Roger Federer (who is president of the ATP World Tour's player council), Rafael Nadal, Novak Djokovic and Andy Murray.
Federer has won their last two meetings but has lost all four times the players have met on clay.
Henman has a 6-6 record against Federer but has lost their last five meetings.
To witness the back-and-forth of their flirtation is like watching Nadal versus Federer on clay.
With Federer out, the path on their side of the draw appears clear for Britain's Andy Murray, who eased past Michael Russell of the United States 6-3 7-5 in their third round match.
Federer had beaten Nalbandian in eight of their last nine meetings including a 6-4 6-0 win in the semi-final in Madrid last year.
So Woods, Federer and Brady - perhaps all the best in their respective sports.
In the other half of the draw, Roger Federer will take on Novak Djokovic in a repeat of their US Open semi-final.
In the men's draw, second seed Roger Federer and world No. 3 Andy Murray both continued their strong starts to the tournament with emphatic victories.
Federer had beaten Falla in straight sets in both of their previous meetings but was almost made to pay for a poor first set, which saw the top seed make a remarkable 21 unforced errors.
And perhaps the high point of the Federer-Nadal rivalry (renewed for the 29th installment on Thursday evening) was their 2008 Wimbledon final, which took four hours and 48 minutes.
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