The two players fight into the tiebreak in the first set and it was 36-year-old Federer showed his dominance, winning 5 points in a row to take a one-set lead.
The second seed continued his form in the second set, breaking to love in the first game and eventually close the set 6-4, cruising to his first win in Shanghai after 2017.
Awaiting for Federer in the third round is Ukraine's Alexander Dolgopolov, who beat Spaniard Feliciano Lopez 7-6(4), 1-6, 6-4.
In the other actions, third seed Dimitrov recovered from a 2-4 deficit in the decider and fought back from 6-3 in the tie-break, saving three match points to defeat American Ryan Harrison 3-6, 6-3, 7-6(6) in a 154-minute fight.
Dimitrov will next meet Sam Querrey, ranking 11th position in the Emirates ATP Race To London, who beat fellow American qualifier Frances Tiafoe 6-3, 7-6(7) on Wednesday.
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