Robredo snapped Fognini's winning streak of 13 straight matches, needing just 62 minutes to dispatch him 6-0, 6-3 for his 12th overall ATP Tour crown.
He is the first Spaniard to win in Umag since Juan Carlos Ferrero in 2010.
Fognini came up short in his bid for a third consecutive championship after winning the Mercedes Cup and the German Open Tennis Championships.
The Italian was seeking his third career title.
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