Fognini, the runner-up last year, broke Inglot early in each set and saved the only break point he faced late in the second set.
The 17th-ranked Italian is looking for his third career title. He won his first two back to back in June.
Guillermo Garcia-Lopez of Spain, who is also looking for his third career title, defeated Russian qualifier Mikhail Biryukov 6-4, 6-1.
Eighth-seeded Denis Istomin of Uzbekistan eliminated Samuel Groth 6-4, 3-6, 7-5, breaking decisively on his first match point when the Australian qualifier returned his forehand long.