Nadal brushed aside 25th seed Gael Monfils 6-1 6-2 6-3 in the night session while earlier in the day Murray overcame number 26 seed Feliciano Lopez 7-6 (7-2) 6-4 6-2 and Federer steamrolled Teymuraz Gabashvili 6-2 6-2 6-3.
Monfils was billed as a tricky task for Nadal, but the 13-time grand slam champion made light of that notion as he tormented and bullied the Frenchman who was reminded of just how far away he still was from becoming one of the 'big boys' on tour.
The world number one began the match with all guns blazing and skipped away to a 4-0 lead.
Monfils was doing very little wrong, as evidenced by the second game which lasted 18 points, included six deuces and saw the Frenchman have three break-point opportunities.
But Nadal had all the answers and was playing tennis on another level as he clinched the first set with minimum fuss.
Monfils did his best to hang in there in the second set, but was broken again in the sixth and eighth games as Nadal stormed to a two-set lead.
The flamboyant Frenchman cut a forlorn figure at times during the contest as he struggled to come up with a strategy to combat the white-hot Nadal.
Monfils put up more of a fight in the third set but it was still nowhere near enough to rein in the rampant Nadal who completed his comprehensive win in just over two hours.
Incredibly, Monfils hit more winners (33-21) but he was badly let down by his 57 unforced errors which included five double-faults and was a tally that more than tripled Nadal's (18).
Nadal will face Kei Nishikori after the Japanese 16th seed overpowered American Donald Young 7-5 6-1 6-0.
Nishikori trailed 2-5 in the first set but won 17 out of the last 18 games to brush aside Young who was hampered by a left shoulder complaint.
Murray was tested early by Lopez in their encounter before eventually triumphing over the Spaniard.
Murray and Lopez exchanged breaks in a tight first set before heading to a tie-breaker, although the Scot had the chance to take the first set quicker as he had seven additional break-point opportunities for the set - five of which occurred across two games Lopez eventually won - compared to his opponent's zero.
However, the tie-breaker was a virtual no contest as the number four seed easily claimed it 7-2 and that was as close as the Spaniard would get to Murray who completed a comfortable straight-sets win on the back of a superior percentage of first-serve points won (86-70) and Lopez having a far higher total error count (77-53).
The reigning Wimbledon champion will now face French lucky loser Stephane Robert who accounted for fellow lucky loser Martin Klizan from Slovakia 6-0 7-6 (7-2) 6-4.
Federer was untroubled during the one hour and 41 minutes he spent on Rod Laver Arena.
The 17-time grand slam champion and sixth seed's emphatic victory came on the back of a professional display as he hit 35 winners and 18 unforced errors.
Gabashvili, the world number 79, never looked like causing a huge upset, and an unforced error count of 33 did him no favours.
A clash against Jo-Wilfried Tsonga awaits Federer, who is into the fourth round at Melbourne Park for a 13th straight year.
Tsonga, the 10th seed, won his all-French encounter against Gilles Simon 7-6 (7-5) 6-4 6-2 at Hisense Arena.
The first set was a gripping affair that saw neither player's serve broken and the tie-breaker followed a similar theme as Tsonga and Simon went point-for-point for the first nine points.
The breakthrough came when Tsonga grabbed a 6-4 lead and Simon would not be able to overcome that buffer in conceding the first set.
From then on Tsonga careered away against a weary Simon who had spent four hours and 26 minutes longer on court than Tsonga in the first two rounds.
Spaniard Roberto Bautista-Agut advanced to his maiden grand slam fourth-round appearance with a 6-2 6-1 6-4 thrashing of French 27th seed Benoit Paire.
Bautista-Agut, who upset Argentine Juan Martin del Potro, swept through in 90 minutes as Paire battled a leg injury and will now play Grigor Dimitrov.
In a battle between two young guns, Bulgarian Dimitrov edged the big-serving Milos Raonic 6-3 3-6 6-4 7-6 (12-10).
In a high quality match, Dimitrov hit 49 winners and just 13 unforced errors in an impressive display.
6-Roger Federer (Switzerland) beat Teymuraz Gabashvili (Russia) 6-2 6-2 6-3
LL-Stephane Robert (France) beat LL-Martin Klizan (Slovakia) 6-0 7-6 (7-2) 6-4
Roberto Bautista-Agut (Spain) beat 27-Benoit Paire (France) 6-2 6-1 6-4
22-Grigor Dimitrov (Bulgaria) beat 11-Milos Raonic (Canada) 6-3 3-6 6-4 7-6 (12-10)
4-Andy Murray (Great Britain) beat 26-Feliciano Lopez (Spain) 7-6 (7-2) 6-4 6-2
10-Jo-Wilfried Tsonga (France) beat 18-Gilles Simon (France) 7-6 (7-5) 6-4 6-2
16-Kei Nishikori (Japan) beat Donald Young (USA) 7-5 6-1 6-0
1-Rafael Nadal (Spain) beat 25-Gael Monfils (France) 6-1 6-2 6-3