Eala, ranked 28th, overpowered Pegula over the final two sets as play resumed in the final suspended after lengthy weather delays on Sunday.
Playing in her second final, after a runner-up finish at Eastbourne last year, the 21-year-old left-hander produced a rock-solid service display and an impressive array of winners to deny third-ranked Pegula a 12th career title and a third this year.
The scoreboard showed a match time of one hour and 45 minutes, but it took nearly 24 hours to complete.
Pegula had won the first set 6-4 and Eala was up 2-1 in the second on Sunday when officials postponed the finish until Monday after lengthy rain delays.
The pair had waited through a three-hour delay before starting, and once the match was halted it was another five hours before officials called a halt for the day.
That also saw the ATP final between 10th-ranked American Taylor Fritz and 19-year-old Spaniard Rafael Jodar postponed.
Pegula opened the action on Monday with a nervy service hold for 2-2.
But she could make no inroads on Eala's serve and Eala broke Pegula in the 10th game to take the set and force a third.
The final set was all Eala, to the delight of a vocal contingent of supporters.
Eala had been enthusiastically cheered all week as she made her way to the final with wins over second-seeded Elina Svitolina, third-seeded former world number one Naomi Osaka and defending champion Leylah Fernandez.
Eala is now projected to rise to a career-high 20th in the world.