Tsonga came from two sets down to force a fifth in the English capital, but it was Murray that came through a 7-6 6-1 3-6 4-6 6-1 winner following just shy of four hours of tennis.
A close-fought first set saw both players secure breaks and ultimately force a tie-break, which Murray won 12-10 as Tsonga's best efforts to take a one-set lead proved unsuccessful.
After putting so much into the first set, Tsonga struggled in the second and it was comfortable for Murray, who recorded a 6-1 success to move into a comfortable position.
Tsonga secured a vital break at 1-2 in the third set, however, before holding three times to force a fourth.
Both players held their opening two service games of the fourth, but a Murray break at 2-3 allowed the world number two to move 4-2 ahead and move within touching distance of the last four.
Tsonga responded once again though, breaking Murray twice in the latter stages to record a 6-4 victory in the fourth.
The Frenchman's energy reserves were fading, however, and Murray quickly breezed into a 4-0 lead in the fifth, before ultimately winning it 6-1 to book a semi-final meeting with Tomas Berdych on Friday afternoon.