The Swiss world number three let out a huge roar after unseeded Frenchman Simon hit a forehand into the net to give him a 7-6 (8-6) 7-6 (7-2) victory.
"To win the biggest tournament in Asia is a treat," said Federer, who lost in the 2010 final to Briton Andy Murray.
"I got lucky to come through the first round after saving five match points. It's been a dream week."
Federer, 33, won the opening set with his only backhand winner down the line.
Simon led 6-5 in the second set and had two set points but two unforced errors allowed Federer a way back and the 17-time Grand Slam winner took advantage.(KH)