The top-seeded Japanese captured his eighth ATP crown, and his first since he won in Tokyo in October.
That was one of two titles Nishikori captured late last year after a breakthrough run to the final of the US Open.
This year, the world number five hadn't made it to a final until this week, but a return to Memphis proved the tonic he needed.
"It feels great," said Nishikori, who became the first man to win three straight titles at Memphis since the tournament began in 1975. "I think I'm going to move here soon."
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Nishikori took charge in the second with a break for a 3-2 lead but the drama wasn't done.
Serving for the match at 5-4, he raced to a 40-0 lead, but Anderson held on for deuce.
After the South African pushed a backhand long, Nishikori sealed the win on his fourth opportunity, when Anderson went wide with a forehand.
"I played one of the best matches I played here," Nishikori said. "I thought it was a great match, so I'm really happy to win today."
His only titles came at the 2011 South African Open and in 2012 at Delray Beach, Florida, where he now resides.