The 24-year-old Slovakian won 2-6 6-1 6-2 in just 90 minutes to stun the world No 15 on his favourite clay surface.
Klizan, world ranked No 111, looked to be heading swiftly to defeat when the Italian broke serve three times in the opening set.
However, from that moment on Klizan took charge by winning 10 of the next 11 games.
The Bratislava-born player, who briefly left the court with a stomach complaint during the opening set, needed just one match point to seal a well-deserved victory.
His only other ATP Tour title came in September 2012 when his final opponent had also been Fognini - on the hard courts of St Petersburg.
It ended a great week for Klizan after he had already knocked out two-time Munich winner Philipp Kohlschreiber and then defending champion Tommy Haas in the semi-finals.
And the new champion said: "I felt very bad and took two tablets because of stomach cramps after the first set. That was a crazy game from both of us."
All three of Fognini's Tour titles have come on clay and, only last month, he beat Andy Murray in the decisive fifth and final Davis Cup rubber in Naples to seal a 3-2 triumph for the hosts.
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