The fifth set followed a similar plot line, lasting 27 minutes as Murray won just one point off the American's serve.
The second semifinal was lined-up after wins by Roger Federer and Tomas Berdych.
The Czech 11th seed was leading by a set and a break of serve when second seed Djokovic withdrew due to an elbow injury.
It's the first time an American man has reached the semifinals at Wimbledon since Andy Roddick in 2009.
The semifinals is shaping up to be thrilling at Wimbledon this year.
Another four chances came and went in game eight as Federer showed grit to go with his grace - the latter in evidence again in the tie-break as he came from 3-0 down to celebrate his 100th Wimbledon match in style.
Murray, who won Wimbledon past year and in 2013, came into the tournament with a hip problem, that interrupted his preparation.
Querrey will now face Marin Cilic--who defeated Gilles Muller 3-6, 7-6 (8/6), 7-5, 5-7, 6-1--in the semi-finals.
However, Murray then found it hard to move freely and 24th seed Querrey eased to victory in the final two sets to claim a 3-6 6-4 (4-7) 6-1 6-1 victory on Centre Court.
For Querrey the win marks his first ever trip to the semis of a slam and he himself seemed to not believe it when speaking post-match to the BBC. Murray has lost his last three five-set matches overall.
Querrey has become Wimbledon's chief giant-killer, having also downed then champion Novak Djokovic in last year's third round. Murray most recently beat Querrey earlier this year, knocking him out of the Australian Open.
Centre Court has a roof, but No. 1 Court does not.