Querrey is the first American man to reach the semi-finals at a major tournament since Andy Roddick was Wimbledon runner-up in 2009.
The 29-year-old from California is second in the aces chart with 99 and a fastest serve of 137mph.
Seven-time Wimbledon champion Federer fired 46 winners and committed just nine unforced errors to get into the semi-finals for the 12th time at the All England Club.
The result might have been different had Murray capitalised on a lead in the second set but, although he won the third, the physical stress took its toll and the Scot fell to a 3-6 6-4 6-7 (4/7) 6-1 6-1 loss.
That snapped Djokovic's 30-match winning streak at the majors.
The reigning Wimbledon Champion has not fared well in Grand Slams this season after earning the world number one ranking at the end of last year. Here are her first statements: "Being the number one is a great responsibility for me. Potentially that can hurt anyone in the game".
Both players impacted this turn of events, as Querrey entered his red-hot mode seen against Djokovic last year and Rafael Nadal in the Acapulco final earlier this year, while Murray's balky hip finally was too much to overcome. "I didn't start my best, I just kept with it, kept swinging away and then just kind of found my rhythm in the fourth and fifth set and then everything seemed to be falling my way then".
Home nation hopes will now rest with Johanna Konta, who on Tuesday became the first British woman to make the semi-finals at Wimbledon since Virginia Wade in 1978.
Indeed, until last year's win over Djokovic, he might have been best known for some of his unusual off-court episodes.
Venus and Serena have also each won one Olympic women's singles title apiece, in 2000 and 2012 respectively.
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