She raced to a 3-0 lead before 23-year-old Belarusian Sasnovich found her range with some lethal backhands and briefly threatened to make it a contest.
Svitolina, however, unleashed a series of powerful groundstrokes to break again and clinch the first set, before running away with the second to claim the title in just over an hour.
"It was a tough, tough offseason," third seed Svitolina, also 23, said on court after the match. "To start with a trophy is always very, very special."
World number 88 Sasnovich, bidding to become the first qualifier to win the title in Brisbane, ran out of gas in her eighth match of the week and only her third career encounter against a top 10 player.
She had stunned sixth seed Kristina Mladenovic in the opening round and defeated last year's runner-up Alize Cornet in the quarter-finals before battling past Anastasija Sevastova in the last four.
"Sorry for my play today," Sasnovich told the Brisbane crowd. "It was an incredible week for Elina - she was better than me and deserved to win. It was a good week for me."
Svitolina, having landed her first silverware of the season, heads to the Australian Open with her eyes fixed firmly on a maiden grand slam trophy. The tournament begins on Jan. 15 at Melbourne Park.
(Reporting by Hardik Vyas in Bengaluru; Editing by Ken Ferris)
