His 2013 championship broke a 77-year drought for Great Britain, and Murray would love nothing more than to follow-up that title after just three years.
If Federer prevails, he will then face either USA 28th seed Sam Querrey, the conqueror of Novak Djokovic in the third round, or sixth-seeded Canadian Milos Raonic.
He has shrugged off questions about the impact of Novak Djokovic's defeat, but this is the first time the Scot has found himself as the highest-seeded player left in a grand slam.
Seven-time champion Roger Federer admits 2001 Wimbledon victor Goran Ivanisevic will prove a formidable opponent in his quarter-final against Marin Cilic even though the colourful Croatian retired 12 years ago.
Murray, who had yet to drop a set in the tournament, looked well on the way to a swift win when a tense Tsonga double faulted in the fifth game to hand a quick break to the Briton. I believed that I could win the match.
"He has won some tough matches here, he's played a lot of tennis and I will need to play well".
Murray then ends the second frame after a 40-30 win in the seventh game, leaving him one set away from sealing off the floundering Frenchman.
Even so, it won't be easy against Tsonga who has rediscovered his best form at Wimbledon after an injury-plagued start to the year. However, as far as Tsonga was concerned, the match had only just begun.
Those fears vanished in a high-quality opening set in which Murray was dragged into an epic 22-point tiebreak despite forging ahead with an early break of serve.
Tsonga threw everything at his opponent and brought up two set points at 6-4, only for Murray to come up with an ace and then a stunning return off a 129 miles per hour serve.
Tsonga of course is best known for his Australian Open triumph in 2008 when as an unseeded player he made it all the way to the final, knocking off some of the best players in the world.
Soares complained: "I feel like I get a warning right away because I am calm". Physically, [if] you're strong, that helps... but mentally, today was a tough match.
"I'm not that interested in what the Press say". I thought I was playing some really good tennis. "Never thought I was going to have such a great career, you know, at Wimbledon ever since I turned up here in '98". "If I was him, it will be a bonus, for sure".
Should an "All Williams" final occur, it would be the first since 2009 when Serena beat Venus in straights sets at Wimbledon.
Victory for the Brit ensures that Murray now moves on to face Czech tenth seed Tomas Berdych in the final four, while seven-times Wimbledon champion Roger Federer faces Canadian sixth seed Milos Raonic on the other side of the draw. Berdych was pushed to five sets in his Round of 16 match so he has to be feeling good about breezing through the young Pouille. The world no. 9 Berdych was able to break Pouille four times in eight attempts. He also equalled Jimmy Connors' all-time match wins record by beating Marin Cilic in the quarters.
And, in the final quarterfinal to be decided, Murray faced a battle for the first time here this fortnight.