Konta, playing in her first WTA final since June last year, did not face a single break point as she surged ahead to claim the opening set before unforced errors crept into her game.
The world no. 47 was leading 4-2 in the second set when sixth seed Sakkari reeled off four straight games to force a decider.
The 23-year-old claimed victory with a forehand winner, guaranteeing her rise into the WTA's top 50 when the new rankings are released on Monday,
She then fell on her back on the red clay and went on to kiss the surface in celebration after being congratulated at the net by Konta, who has also enjoyed a largely positive week.
The Briton's French Open preparations have been boosted by her four victories in Morroco, the first time she has claimed more than two WTA main draw wins in a row on clay in her career.