Five-time runner-up Murray served out for a 6-4, 6-2, 6-4 win over Querrey, who has had recent form against the No. 1-ranked player in the third round of a major.
It was Querrey who ended Novak Djokovic’s impressive Grand Slam run in the third round at Wimbledon last year. At that time, top-ranked Djokovic had won four straight major titles – Wimbledon and U.S. Open in 2015 and Australian Open and French Open in 2016.
Murray, who gained the No. 1 ranking for the first time ever last November, is still in contention in Australia while both Djokovic and Querrey are out.
Six-time Australian Open champion Djokovic had a shocking second-round loss to Denis Istomin on Thursday.
Murray took no chances against No. 31 Querrey, fending off a break point in the decisive game in the first set and then staying in control of the 1-hour, 59-minute match.
He injured his right ankle in the second round, and said he was hesitant at first on Hisense Arena before settling into the match against Querrey.
“I felt better and better as the match went on in terms of my movement,” Murray said. “I was moving well at the end – it was very positive.”
The last two Americans in the men’s draw lost within an hour of each other. No. 23-seeded Jack Sock lost 7-6 (4), 7-5, 6-7 (8), 6-3 to No. 12 Jo-Wilfried Tsonga, the 2008 Australian Open finalist.
U.S. Open champion Stan Wawrinka was twice broken while serving for the match before finishing off a 3-6, 6-2, 6-2, 7-6 (7) win over Viktor Troicki.
Wawrinka, the 2014 champion at Melbourne Park, reached the round of 16 for the fifth consecutive year and will next play Andreas Seppi, who beat Steve Darcis 4-6, 6-4, 7-6 (1), 7-6 (2).
Murray next plays Mischa Zverev, who had a 6-1, 4-6, 6-3, 6-0 win over Malek Jaziri.
Women’s No. 1 Angelique Kerber had a straight-sets win for the first time in her first Australian Open title defense, starting her 6-0, 6-4 third-round victory over Kristyna Pliskova.
She beat the other Pliskova twin, Karolina, in the final of the last U.S. Open to capture her second career Grand Slam title. Her first was here at Melbourne Park 12 months ago.
Kerber will next play 35th-ranked CoCo Vandeweghe, who reached the fourth round in Australia for the first time with a 6-4, 3-6, 7-5 win over 2014 semifinalist Eugenie Bouchard.
Bouchard, ranked 47th ahead of the tournament, hasn’t gone past the third round of a Grand Slam tournament since slipping and falling in the locker room during the 2015 U.S. Open.
Eighth-seeded Svetlana Kuznetsova was broken twice while serving for the match before finally finishing off former No. 1-ranked Jelena Jankovic 6-4, 5-7, 9-7 in 3 hours and 36 minutes.
Two-time major champion Kuznetsova will next play No. 24 Anastasia Pavlyuchenkova, who beat No. 11 Elina Svitolina 7-5, 4-6, 6-3.
Australian Open organizers were briefed by Victoria state police over an incident in downtown Melbourne where a man deliberately drove into a street crowded with pedestrians, killing three people and injuring 20. Police said the incident, which occurred about three kilometers (two miles) from Melbourne Park, had no links to terrorism.
Organizers said the police had contained the incident and an offender had been arrested.
“Be assured there is no threat to the precinct,” a statement read.