The world number two was quick to impose his ability on Harrison, going a break up in the first game.
Nadal then won a simple point in his opening service game, but a double fault brought Harrison level at 15-15.
A further double fault meant 40-30 but Nadal's next serve wrapped up the second game.
Harrison got on the scoreboard at 2-1 with a comfortable service game, but struggled to return Nadal's serve, slipping further behind.
Nadal found himself at 5-3 ahead, but Harrison managed to hold his serve to force him to serve for the set, which he did comfortably.
A light drizzle interrupted play at the start of the second set after Nadal had again broken, with Harrison pushing a forehand wide to give the Spaniard two break points.
It was soon 3-1 to the former Wimbledon champion as strong serving and a number of forehands confirmed a routine game.
Nadal then broke again to move 5-2 ahead after Harrison netted on a second serve.
Serving for the second, the 2010 US Open champion gathered three set points on his serve to move into a two-set lead.
Harrison, who won only 29% of points on his second serve, was soon 3-0 behind in the third set after throwing away a 40-0 service game to give Nadal another break.
The American won his next service game but couldn't stop Nadal and was soon 5-2 down and facing match point.
Nadal wrapped up the win after Harrison stumbled.