The South African followed up his opening-round victory against Dominic Thiem to make it two wins in as many matches.
Anderson was in incredible form as he whitewashed Nishikori with an opening-set bagel which was wrapped up in 31 minutes.
The world No 6 only dropped four points on serve in the first set as he powered his way into the lead.
He carried the momentum into the second to go 5-0 up by stunning the Japanese star, who had beaten Roger Federer just two days previous.
But Nishikori got the biggest roar of the afternoon from the London crowd when he finally got on the board, holding serve, which only delayed the inevitable.
Anderson then served out the match which lasted just one hour and three minutes.
Anderson's result means Federer will be knocked out of the competition if he fails to beat Thiem tonight.
Head-to-head results come into play if two players in a group are tied on points which means Federer most not lose when he takes to
"It is one of the best matches I have ever played," Anderson said on court after his win.
"I knew I had to come out and play really well. Kei is an exceptional player.
"You wait a whole year to play a match like this so to do it here feels fantastic.
"I remember as a kid watching this as a young child.
"It was a very unique looking court and for me to be here this many years later means a lot to me."
Anderson will be guaranteed a place in the semi-finals if Thiem beats Federer.