Sabalenka made a flying start to the match, breaking Gauff's serve in the opening match.
Things were comfortable for the world number one after that, with her not facing a single break point on her way to sealing the opening set 6-2 in 38 minutes.
Gauff started the second set well, forcing a first break point of the match in the second game, but she wasn't able to convert it.
After that, it looked like Sabalenka was going to secure the Sunshine Double in straight sets, with Gauff having to fight off break points at 2-2 and 3-3, barely withstanding serious pressure.
However, she stepped up her game when it mattered most, taking advantage of some errors that had crept into her opponent's game and fighting back from 30-0 down to finally break serve and win the second set 6-4, taking the final into a decider.
Gauff had sent the home crowd wild, but Sabalenka quickly took the wind out of their sails by racing into a 2-0 lead in the final set.
She never looked like losing her advantage after that, and broke Gauff again at the end of the decider to seal a 6-2, 4-6, 6-3 triumph.
Her victory sees her become the fifth player in the history of women's tennis to seal the Sunshine Double, and just the third to win more than 10 WTA 1000 titles.
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"I know Coco quite well," Sabalenka said. "I know that she's not going to, like, give me this final easily. I knew that she's going to be fighting, she's going to be moving well, she's going to be trying to put literally every ball back on my side.
"I lost a couple of opportunities in that second set, but I was just trying to stay mentally positive going into the third set."
"What can be better than this month?" said the world number one, who, along with two prestigious titles, acquired a new puppy and got engaged to boyfriend Georgios Frangulis.
Gauff was also feeling grateful after a rocky March that saw her withdraw from her third-round match at Indian Wells with a nerve issue that caused "scary" pain in her left arm.
She had said after a dominant semi-final win over Karolina Muchova that she was making progress with the inconsistencies in her serve and forehand.
And after considering skipping the event, the 22-year-old was thrilled to reach the final for the first time.
"I don't think with the conversations we had earlier that this was the result we were expecting," she said at the trophy presentation.
"So although it sucks to not come out with a bigger trophy today I had a lot of joy this week and that's something that I'm taking away from this the most."