Federer, Murray, Azarenka hit top gear at Aussie Open
Switzerland's Roger Federer serves during his men's singles match against Russia's Teymuraz Gabashvili on day six of the 2014 Australian Open tennis tournament in Melbourne on January 18, 2014 - by Paul Crock
As cooler temperatures consigned this week's heatwave to memory, Federer swept past Russia's world number 79 Teymuraz Gabashvili 6-2, 6-2, 6-3 in what is his record 57th consecutive major tournament.
Murray moved smoothly past Spain's Feliciano Lopez and Maria Sharapova came through a test against French challenger Alize Cornet before reaching the fourth round.
In the evening session, Azarenka showed little mercy to unseeded Austrian Yvonne Meusburger, winning 6-1, 6-0 to set up a rematch with Sloane Stephens after their controversial semi-final last year.
Federer, with an unsurpassed 17 Grand Slam titles but now aged 32, last year lost in Wimbledon's second round and in the last 16 at the US Open, raising doubt about his ability to win more major titles.
But the Swiss, who said he was comfortable with his new, bigger racquet and with Swedish great Stefan Edberg in his corner, hoped his 2013 difficulties were now behind him.
"It was a tough year last year and it took some time to figure out what I needed to do to feel better and to get my confidence back, because that's what I thought it was mostly," said Federer, seeded six.
"For the last four to five months I feel that I'm back to normal again and at least I feel I've done the work to catch up and haven't had any setbacks, so it's very positive."
Federer, who now faces France's Jo-Wilfried Tsonga, said he was happy with his first week's work in dismissing James Duckworth, Blaz Kavcic and now Gabashvili without losing a set.
"Now the draw is getting extremely difficult... but I'm looking forward to it... I've done the work and haven't lost a set so far," the four-time champion said.
Wimbledon champion Andy Murray continued his recovery from back surgery with another fluent win, downing Lopez 7-6 (7/2), 6-4, 6-2 to reach the fourth round also without dropping a set.
"Today was a big step up for me. Feliciano is a top-30 player. He's a tricky opponent to play," Murray said.
Russia's Sharapova was less impressive and she struggled for a second successive match before ousting Cornet.
The third seed, on her way back after a shoulder injury, was made to work for the win before coming through 6-1, 7-6 (8/6). She also had trouble putting away Italy's Karin Knapp in the second round.
Sharapova will next play Slovakian seed Dominika Cibulkova, who beat Spain's Carla Suarez Navarro. Serbia's Jelena Jankovic won against Kurumi Nara to set up a meeting with Romanian Simona Halep.
But former world number one Caroline Wozniacki took a tumble when she was shocked by the unheralded Garbine Muzuruga, 20, who extended her best ever Grand Slam run.
Next up for the emerging Spanish star is Polish fifth seed Agnieszka Radwanska, who came from a set down to oust Russia's Anastasia Pavlyuchenkova.
Stephens beat Elina Svitolina to cue up the rematch with Azarenka, who drew criticism after last year's semi-final when she suggested she took a medical timeout to calm down. She later said she had an injury.
"That has nothing to do with this year. I don't even remember half the stuff that happened. It's okay," said the 20-year-old American.
France's Stephane Robert became the first "lucky loser" to reach the Australian Open fourth round when he beat Slovakia's Martin Klizan. It was the first match between two lucky losers at this stage of a Grand Slam since 1973. Robert, 33, will now play Scotland's Murray.
Bulgarian Grigor Dimitrov won impressively against big-serving Canadian Milos Raonic and Spain's Roberto Bautista Agut upset Frenchman Benoit Paire.
Meanwhile, Kei Nishikori reeled off the last 10 games against Donald Young to end American interest in the men's singles and go into a match-up against Rafael Nadal or Gael Monfils.
And Tsonga, runner-up in 2008, ended the campaign of fellow Frenchman Gilles Simon.