After the first five games went with serve, Granollers stumbled, a double fault gifting Federer three break points.
He needed only one and the Swiss star never looked back.
Federer said: "I thought I was sharp, I knew what I wanted to do and I was able to do it.
"He was going to come in, so I thought I would rather hit a volley than a passing shot – when the courts are so fast, you want to play offensive."
Juan Martin Del Potro wasted little time in beating Somdev Devvarman 6-4 6-4. The Argentine saved three break points in his opening two service games, but was otherwise largely untroubled.
The former US Open champion was taken to a deciding set tie-break by Cypriot Marcos Baghdatis in a first round, saving three matches points.
ICE HOCKEY Sheffield take a two-goal advantage over Braehead Clan into next Tuesday's second leg of the Challenge Cup semi-final after last night's 4-2 win.