Nadal needed just one break in the opening set as he won four of the opening five games, racing into a 4-1 lead which he never looked like letting go.
There was scant hope for Vesely in the second set too as Nadal continued to dominate on his own serve, making the first break to love in the fifth game before breaking again in the final game of the set to take it 6-3.
The number two seed finally slipped up in the third set when Vesely broke to move into a 3-2 lead, but Nadal responded in kind immediately to restore parity.
The world number 93 did save two match points to keep himself in the contest, but it was only a temporary reprieve and Nadal took full advantage of his third to wrap up the victory.
Nadal is looking for his third title at SW19, where he has not won the trophy since 2010.