The Scotsman rallied in a 6-4 6-3 7-6(6) win over the big-swinging Anderson, to keep his defence of his title in check.
The 27-year-old Briton returned sharply and drew the 6ft8 Anderson into rallies to impose his game and stretch his run on Wimbledon’s grass to 17 successive victories.
Anderson only managed to break Murray’s service just once as the rain forced the centre-courts roof to be closed with the reigning champion 3-0 up in the second set.
The South African pushed the third set to a tie-break and even managed to get a set-point before Murray bounced back with three straight points to reach his seventh successive Wimbledon quarterfinal.
“When it was outdoors I played very well and was in a good position, but when we came indoors he was striking the ball better and serving better and I was dropping shorter,” Murray told BBC Sport.
“That meant there was a lot more running at the end because he was playing very well.”
