The 29-year-old - the first American male since Andy Roddick in 2009 to make the last-four of a Slam, came through on his 42nd attempt, the most by a player, winning 3-6, 6-4, 6-7 (4), 6-1, 6-1 in 2 hours and 42 minutes.
"I didn't start my best but I kept with it, swinging away, then really found a groove in the fourth and fifth set", Querrey said.
Murray says he doesn't deserve to stay at the top though after the year he has had.
From there, Querrey hit a simple drop shot that Murray had no chance to return and let out an emphatic roar in celebration.
Querrey, ranked 28 in the world, will play against Marin Cilic of Croatia in the semifinals on Friday. He lost his next match to Canadian Milos Raonic. I predicted that Cilic would have a good run, and he's proving to do so.
Andy Murray is a two-time Wimbledon champion. Querrey dished out an impressive performance to beat Murray 3-6, 6-4, 6-7, 6-1, 6-1. This will be the 37-year-old American's 10th Wimbledon semifinal and 22nd at all majors. "Yeah, I guess the break is something that I will have to consider right now".
"I didn't start my best, but I just kept with it", Querrey continued.
He will face Berdych for a place in the 11th Wimbledon final of his career. "I think Venus and Serena have won about four each".
Marin Cilic, the seventh seed, made it past Gilles Muller, the 16th seed, also in five sets.
A year after ending Novak Djokovic's incredible streak of 30 straight wins at majors, Querrey has defeated the World No. 1 and Wimbledon defending champion for the second year in a row, this time against Andy Murray.
Although British hope Murray was limping around Centre Court, nursing a clearly painful hip injury, Querrey would not be distracted, and put the foot down to reach the semi-finals with a shock 3-6 6-4 6-7 (4) 6-1 6-1 victory.
"I'm happy my dream run continues, we will see what happens next", the 18-time Grand Slam victor said.