The 61-st ranked Lu was able to do what many others have failed to do and subdue Anderson's serve, breaking the South African twice in the second set after edging out a first-set tie-breaker.
The Taiwanese player was solid throughout and capitalised on errors made by his opponent as Anderson struggled to get into the encounter, with Lu winning 90 percent of points on his own serve and withstanding 12 aces off the racquet of Anderson.
"He's a great player, and you cannot give him any chances," Lu said after the match.
"All the match I was really concentrating … this match has made me get a little bit of confidence back for the year."
Lu will face fifth-seeded Adrian Mannarino of France in the quarter-finals.