Svitolina secured her second consecutive victory over the world number four in a gruelling three-hour encounter, having previously beaten Gauff in straight sets at last month's Australian Open quarter-finals.
Two-time Grand Slam champion Gauff struggled with double faults throughout the opening set as Svitolina seized control, breaking decisively to claim it 6-4.
Gauff roared back in the second set, displaying her trademark fighting spirit to force a tiebreak.
The American then saved four match points in a breathtaking 15-13 tiebreak thriller, keeping her hopes alive and electrifying the Dubai crowd.
The momentum swung back and forth in the decider, with the ninth game proving pivotal as it repeatedly went to deuce. Svitolina eventually held her nerve to edge ahead 5-4 before serving out the match to seal a hard-fought victory.
"I'm speechless after that fight. I was really trying to put myself out there, playing as if there was no tomorrow," Svitolina said.
"It's really special to be in the final again after a few years. Coco is such a big fighter. I was expecting her to come back in the match. She's won so many big tournaments. I'm very pleased with the fight and the win," she added.
Pegula shook off a first-set stumble to defeat fellow American Amanda Anisimova 1-6, 6-4, 6-3 in the other semi-final.