The match lasted only 57 minutes and the Swiss got the best out of his break point opportunities as he managed to convert 5 out of 6.
The 19 year old Kudla had his chances in the first set, but he failed to take them. The second set was entirely in dominance of the former world no.1, who got off to a quick 4-0 lead. He only allowed his opponent one game at the end, taking it 6-1 in 25 minutes.
In round three, Federer will face Canadian Milos Raonic, who defeated Carlos Berlocq of Argentina 6-4 6-2.
Raonic will be a good test for Federer. The Canadian is on form this year with a stellar 15-2 match record. He has already won two titles (San Jose, Chennai) and was the finalist in Memphis, where he lost to Jurgen Melzer.