The No. 3 seed defeated a fellow former champion in Connecticut.
The No. 4 seed faded badly in both sets.
A 46th career meeting with Novak Djokovic awaits in Sunday's final.
The Serbian is one win from the career sweep of Masters 1000 events.
Milos Raonic and Pablo Carreño Busta fell to quarterfinal defeats.
Federer is scheduled to meet Stan Wawrinka on Friday night.
The two are slated to meet each other in a quarterfinal later Friday.
No other men's matches were completed before a second lengthy rain delay.
Caroline Garcia was also an upset victim.
Both battled through heavy rain that wreaked havoc on the Thursday schedule.
The 23-time grand slam champion lost just three games.
The former Cincinnati champion needed three sets for her first round win.
The Scot rebounded from a woeful first set but struggled again in the decider.
Each won in quick straight sets.
The South African beat Dimitrov for the first time in six years.
Karolina Pliskova and Julia Goerges also won their openers.
The world No. 5 seeks a fourth title of the year.
The 30-year-old Romanian lost just one game to Maria Sakkari.
In winning his eighth career title, Fognini denied the great Argentine another victory on hard courts.
A win on Sunday would be the biggest ever for either player.