The world number 31 faced a set point against the unseeded Australian but held her nerve, going on to win nine consecutive games in the WTA 500 tournament at OCBC Arena.
It was the 24-year-old Canadian's first title since the Japan Open in October and the sixth WTA title of her career.
"Throughout the year, it's been a lot of hard work in finding the right balance between attacking and defending," Fernandez said.
"Today, everything just kind of clicked in the right place at the right time."
Fernandez reached the final after downing top seed Mirra Andreeva in the quarter-finals and coming from a set down to beat 25th-ranked Maja Chwalinska in the semis.
Gibson appeared in her first career WTA final and held her own during the early stages of the match, twice recovering from service breaks and setting up set point at 5-4 on Fernandez's serve.
But the Canadian dug deep to hold before wearing down Gibson and taking the opener 7-5.
The second set was no contest as Gibson committed a number of unforced errors and dropped her first three service games.
With Fernandez serving for the match, Gibson put a return into the net to hand her the title.
"Talia is a fighter, and she found a way to break me a few times. I got a little bit frustrated and overthought too much in those moments," Fernandez said.
"So when I was facing that set point and those break points, I just told myself to think of the ball and let my instincts take over.
"I wasn't thinking of where I needed to hit it. Just hit the ball and trust that my training is going to pay off, and thankfully today, it did."
