On a cool day in Melbourne, the men's number one and women's top seed Angelique Kerber both hit a hot patch of form as the final rounds beckoned.
Murray will have watched from the sidelines as second seed Djokovic, his conqueror in four Melbourne finals, suffered a stunning defeat to 117th-ranked Denis Istomin on Thursday.
Querrey also shocked Djokovic at Wimbledon last year but Murray, made a knight in Britain's New Year honours, never looked like slipping on any banana skins in round three.
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Murray put Querrey away 6-4, 6-2, 6-4 in just under two hours, winning 77% of points on his first serve and facing only three break points in a clinical display.
The Scot also showed no signs of discomfort in his right ankle, after he rolled it painfully during his second-round win over Andrey Rublev.
“I felt better and better as the match went on in terms of my movement,” he said. “The ankle was a little sore and I was a little tentative at the start but it got better and better through the match.”
Next up for Murray is an assignment with Mischa Zverev, the elder brother of highly-rated German teen Alexander who came through in four sets against Tunisia’s Malek Jaziri.
The winner of that meeting will play either Roger Federer or Tomas Berdych, the old Grand Slam rivals who will play the night match on Rod Laver Arena later.
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Stan Wawrinka, the 2014 champion, survived a four-set tussle with Viktor Troicki 3-6, 6-2, 6-2, 7-6 (9/7) and now faces Italy's Andreas Seppi, who ousted Steve Darcis of Belgium.
Former finalist Jo-Wilfried Tsonga also came through in four sets against Jack Sock and will play either Australia's Bernard Tomic or Briton Dan Evans.
In the women’s draw, Kerber finally got into her stride with a 6-0, 6-4 destruction of Kristyna Pliskova, the 58th-ranked twin sister of Czech fifth seed Karolina.
The German defending champion was an early loser at both of her warm-up tournaments and was taken to three sets in unconvincing wins in round one and two.
Djokovic knocked out of Australian Open
But Kerber clicked into gear against Pliskova, winning in just 55 minutes to set up a last-16 clash with America's Coco Vandeweghe, who ousted Canadian starlet Eugenie Bouchard.
"I'm looking forward to the next one. Yeah, I think that I find my rhythm to the tournament now," said Kerber.
Svetlana Kuznetsova outlasted fellow veteran Jelena Jankovic 6-4, 5-7, 9-7 and will next play fellow Russian Anastasia Pavlyuchenkova.
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