The world number one looked in good touch in New York and was able to manipulate the game almost immediately.
Phau produced some nice strokes at regular intervals in the first set but he could not keep Federer at bay and his serve was broken on two occasions in the opener.
Federer made no mistake after seizing the advantage and was able to comfortably secure a 6-2 win.
The first seed did not have it all go his way in the second set and he was made to fight for the crucial break of serve against his German opponent.
Phau struggled to trouble Federer when returning his serve and the underdog was soon two sets behind.
Federer relaxed in the final set and the crowd were treated to plenty of entertaining rallies, with both players pulling off some marvellous shots.
However, Phau lost the battle of the brains, with Federer's superb tactical play enough to give him a 6-2 win in the third set and confirm his place in the next round of the tournament.