Svitolina twice battled from a break down to level a tight first set at 4-4, and the Ukrainian held on under huge pressure during exhausting rallies to get ahead in the ninth game with some powerful hitting.
A couple of untimely double faults from Gauff's racket in the next game gifted Svitolina the opening set, and the 31-year-old dialled up the intensity late in the next set to go within touching distance of a third Rome title.
Gauff, the reigning Roland Garros champion, held on bravely until 5-5 in the second set and then broke with a reflex volley at the net after a shot that clipped the netcord unsettled Svitolina and forced her into making a flat return.
That joy was short-lived as Svitolina broke back immediately, but Gauff raised her game in the tiebreak to drag the match into a deciding set, where there was little to separate the duo after the opening four games.
A backhand error from Gauff meant Svitolina sealed a vital break in the fifth game, and the Ukrainian pounced again for a double break, before holding her nerve in a tense finish to secure victory on her third matchpoint.
Svitolina will now bid to win her first Grand Slam title at the French Open, which gets underway in Paris on May 24th.