Kudermetova, 23, did not drop a set in six matches on the way to the championship at the season's first clay-court tournament -- a feat last accomplished here by Serena Williams in 2012.
Kovinic, also seeking her first title, sailed a forehand long on match point, making the fifth first-time winner this season on the WTA.
"I really enjoyed the play here," Kudermetova said to the few dozen people watching as she held the championship trophy up high.
The tournament was closed to the general public because of the coronavirus pandemic. It was canceled last year.
Matches were also shuffled to a secondary court with the main stadium undergoing a $50 million renovation.
None of that mattered to Kudermetova, who'll cherish this win as if she played in a full house.
"Of course, it means a lot," Kudermetova said. "I'm really happy and proud of myself at my first title."
Kudermetova didn't feel confident when the week began. Her only other appearance in Charleston was first-round loss in 2019 and she wasn't sure how she'd perform on the slower surface.
On Saturday night, Kudermetova had trouble calming her nerves at the prospect of her first tournament crown.
When she stepped on the court, though, she channeled her performances of the past week to take control against Kovinic.
"It's an amazing week for me," she said. "I played really well. I think I deserved this trophy."
Kudermetova, the 15th seed, relied on her serve and forehand to push past Kovinic, of Montenegro, who had defeated three seeded players to advance to the final.
Trailing 3-2 in the opening set, Kudermetova fought off three break points to hold serve, then took three of the final four games.
Kudermetova trailed again in the final set 2-1, but rallied again. She let out a scream when she won a point at deuce in the fifth game, which she subsequently won to go ahead 3-2.
Kudermetova had an ace clocked at 123 mph to win the next game. She closed things out a few minutes later. Along with the trophy, she won her choice of a new Volvo SUV. After the award ceremony, Kudermetova walked over to where four Volvo models were parked, looking like a car buyer trying to make a smart decision.
Kudermetova had heard about the winner receiving a vehicle, "but it's means more to take the title than to get a car."
The tournament held a groundbreaking at the old stadium court -- now just a skeleton with a green clay surface -- a few hours before the final. The stadium had been unchanged since the event moved from Hilton Head Island to Daniel Island in Charleston starting in 2001. Ben Navarro, owner of Charleston Tennis LLC, which runs the tournament, is planning on having a packed stadium next year.
Navarro's daughter, Emma, lost to Kudermetova in the second round this week.
"I know that I will be coming back," said Kovinic, a 26-year-old who played in her first final since 2016.