When asked whether his win over Murray was one of the biggest of his career the South African replied "definitely".
The 25-year-old saw off world number four Murray in straight sets 6-3 6-1.
"I knew what I had to do today and thought I came out and played really well, played the way I wanted to play," Anderson added.
"He definitely gave me a few free points here and there, but it's always tough putting away opponents, especially when they're as good as him."
Anderson will now face 14th seed Stanislas Wawrinka or American qualifier Michael Russell.