The top seeded Swiss, chasing a record-equalling ninth singles title held by Martina Navratalova, enjoyed serene progress through the first two sets.

He took them 6-2, 7-6(5) and then held a match point in the third.

But the South African Anderson held his nerve and then broke to seal the set 7-5 and then won the fourth 6-4 as his serve proved increasingly dominant.

The match entered epic proportions in the fifth before Anderson sealed the decisive break at 11-11.

He then served the match out to seal a 13-11 set win in a match lasting 4 hours 13min.

Anderson will now face American John Isner in his first semi-final at the grass court Grand Slam event.

Isner defeated Canada's Milos Raonic 6-7, 7-6, 6-4, 6-3.

Serbia's Novak Djokovic also reached the first semi-finals since he won the event in 2015.

He enjoyed a 6-3, 3-6, 6-2, 6-2 victory over Japan's Kei Nishikori.

"It feels great to be in the last four of a Slam," Djokovic said afterwards.

"I've been building in the past couple of weeks. 

"The level of tennis has been going up in the past couple of months and tournaments."

Spaniard Rafael Nadal also won an epic five set battle today against Argentina's Juan Martin del Potro for the right to face Djokovic in the semi-final.

The two-time champion Nadal reached the Wimbledon semi-finals for the first time since 2011 after a 7-5, 6-7(7), 4-6, 6-4, 6-4 success.