Nishikori, who is the defending champion at the eight-man event, needed just over two hours to see off the 20-year-old Thompson.
Having taken the first set courtesy of a lone break, Nishikori let it slip in the fourth game of the second set, with Thompson carving out a break and going on to secure the set.
The deciding set required a tiebreaker to separate the two players, with Nishikori edging out his less experienced opponent 7-4.
"Conditions made it tough to play," the world number five said after the match.
"It was difficult for me to be aggressive. But I played a good tiebreak and I'm happy to win today."
He added: "I had a good start here last year, and I did well last season. I'm coming in with a lot of confidence.
"I've had good off-season training and hopefully I can have another good season.
"Jordan was playing well, especially in the second set, he was not missing much and going for his shots."