The in-form Anderson, who entered Indian Wells at a career-high world number 18 following back-to-back hard-court finals in Delray Beach and Acapulco, recorded his 150th match win and his first in four matches against Wawrinka.
Wednesday’s victory was also Anderson’s fifth career win against a top 10 player.
Seeded 17 for the tournament, Anderson needed two hours 19 minutes to upset third seeded Wawrinka and progressed into his second straight quarter-final appearance in Indian Wells.
“My game-plan coming out was to be aggressive,” Anderson said after his win.
I played Stan [Wawrinka] a few times, the most recent in Shanghai where I lost in a close match and I knew just being quite aggressive and not giving him too much rhythm from the back was the way to go.”
Wawrinka did not face a break point through his first two matches this past week, but lost serve four times against Anderson.
The 28-year-old Swiss had forced a decisive set, after battling from down an early break in the second, but then lost the opening service game of the third set and was broken again at love in the fifth game.
It does not get much easier for Anderson, however, as he will now meet four-time champion Roger Federer in the quarter-finals on Friday.
The two have met once before, last year at the ATP masters in Paris which Federer comfortably won 6-4 6-4.
The 27-year-old South African knocked out another former champion, Lleyton Hewitt, in his second round opener earlier this week.
Anderson admitted that Federer would be a tough task but added that he was ready for the challenge.
“Roger is going to be tough and sort of speaks for himself,” Anderson said.
“There is not too much I can add from that. I have to come out and focus on Friday and just do what I have been doing. I feel like I have been playing good tennis, and I’m going to definitely continue that on Friday.”
Neville Godwin, Anderson’s coach, said he was delighted with the way Anderson performed.
“Kev played really well! He stayed patient but yet played aggressive,” Godwin said.
“Kevin served great in the third set and kept his nerve really well despite the disappointment of losing the second set.”