The former world number one, who had already booked his place in the World Tour semi-final, looked likely to storm the first set until Fish brought the contest back to serve in order to keep himself in the match.
As the set continued Federer found his stride and executed his shots with such precision that forced his American opponent to drop back.
While Fish attempted to pile pressure on the 30-year-old, it wasn't enough to shake the world-ranked number four and Federer took the set 6-1.
Although the Swiss pro took a comfortable lead, his 29-year-old competitor fought back impressively to challenge the second set.
Despite the world number eight initially relinquishing the set point, Fish remained composed and drew level with the match favourite with 6-3.
The six-time Wimbledon champion regained control of the contest in the third set and quashed any chance of Fish producing a comeback. The Paris Masters champion finished off the match on 6-3.