The most gripping of the four quarter-finals saw world number four Murray reach his fourth successive semi-final with a 6-7 (5/7), 7-6 (8/6), 6-4, 7-6 (7/4) win over Spain's David Ferrer on Centre Court.
Murray, hoping to end Britain's 76-year wait for a male singles champion at Wimbledon, is now just one win away from becoming the first British man to reach the All England Club final since Bunny Austin in 1938.
"Ferrer is a great player. He's an unbelievably hard worker. I just played a bit better at the end of the sets," Murray said.
"During the fourth set rain delay I went for a shower and threw some cold water on my face. It was a very intense atmosphere.
"If I lost that set it was going to be a very tough match. Tsonga will be tough, he's serving very well, and I'll have to play very well."
Tsonga reached the semi-finals for the second successive year with a 7-6 (7/5), 4-6, 7-6 (7/3), 6-2 win over German 27th seed Philipp Kohlschreiber.
The 27-year-old, who has lost five of his six meetings with Murray including on grass in the 2011 Queen's final, knocked out Federer in last year's quarter-finals after being two sets to love down before losing to Djokovic in the last four.
"I am happy to win and to get a second chance at a semi-final," Tsonga said.
"Philipp played very well. He served well and was the better player from the baseline. It was tough out there."