With both players boasting phenomenal serving power, it would always come down to mental strength and Querrey edged his opponent in that department in a gruelling five-set affair which lasted three hours and seven minutes. This time a year ago, he took a big five-set win over Bernard Tomic and with a style that plays points quickly, he could put Murray under pressure that way.
And the defending champion rates his next opponent, the unseeded Frenchman Benoit Paire.
Despite progressing in straight sets, Murray's victory was far from straightforward, with Paire's tendency to attempt the ambitious occasionally bearing fruit and testing the world number one.
In the second set, Murray went up quickly to 2-0 but Paire - who persisted with his unpredictable and entertaining mix of drop shots and baseline winners - clawed his way back, leaving Murray looking a little confused and perplexed before he pulled himself together, aided partly by some errant play from Paire, to win 6-4.
Then though, Murray struck - breaking Paire with a brilliant retrieval virtually under the net, and then saving an incredible four set points to take the set.
However, the Bulgarian has yet to win in five encounters against the game's most successful player.
The second Monday of Wimbledon is one of the most famous days in tennis, as the only one of the four Grand Slams that schedules the last 16 men and women together on the same day.
GETTYAndy Murray's injury was the reason for his Wimbledon defeat to Sam Querrey says Henman
"I'm in the quarter-finals of Wimbledon - I don't feel calmer this year than I did in previous years", he said. "To play Murray on Centre Court will be a good experience". "However, now I am doing a great job - let's hope it lasts".
"I mean, what can I say?" We have (Victoria) Azarenka, who has won two grand slams.
"She's a very good player". Murray has won 10 of his last 11 matches on grass court.
Nadal said Muller's powerful serve and crisp volleys make him "uncomfortable" to play. "I think she made the last eight in Paris, as well", said Konta.
"I think I'm playing, I guess, with the mindset of just trying to get better, like I have done every other match I've played in my career, every other tournament I've played as well". "It's something different to play Murray in Wimbledon", he said.
Reigning men's champion Andy Murray has seen his preparation in the build-up to the defence of his title hindered by a hip injury.
Williams, a vocal advocate for Wimbledon's switch in 2007 to equal prize money for the genders, said about the court assignments: "I'm sure that the women ... would want more matches on Centre or Court No. 1 over the whole fortnight". There are no real weak spots on his armour, as you can expect from the world number 1, save for his weak second delivery. The start time of 1pm, already you see fans struggling to get into Court One and Centre and that's not just corporate hospitality.
Sunday was a rest day for the players at Wimbledon, but it was a hectic one for the ground staff as they tended the grass courts of the All England Club, which have come under scrutiny during the first week of the tournament.