The 26-year-old from Cairo scored a 7-5 6-3 victory over Greece's world No.7 after both won their semi-finals earlier in the day.
Sakkari began the day by beating Danka Kovinic 7-5 6-2, while Sherif earned her place in the title match by battling to a 6-4 3-6 6-4 victory against Ana Bogdan.
The final surprisingly went the way of Sherif, who first entered the WTA top 100 in August of last year and has reached a high of No.44 in the rankings.
She began this week at No.74 but will climb again after the biggest success of her career.
"It means a lot for my country," Sherif said. "I'm just thrilled and happy. This was never expected."
Sherif, who studied sports medicine at Pepperdine University in Malibu, California, was understandably weary after her two wins on Sunday (AEDT). Saturday's (AEDT) play had been cancelled because of rain, forcing the players to take to the courts twice on finals day.
"I'm exhausted," Sherif said. "Today was a very tough day for me, many hours on court. I'm very happy that I pulled it off. I had to dig very deep."
At the Tallinn Open, Monday's (AEDT) final will be a tantalising tussle between Anett Kontaveit and Barbora Krejcikova.
World No.4 Kontaveit was a 6-4 6-4 winner against fellow Estonian Kaia Kanepi in their semi-final.
Czech Krejcikova, who won last year's French Open, saw off No.2 seed Belinda Bencic from Switzerland 6-7 (5-7) 7-6 (7-2) 6-2.