Konta, who had never won an elite WTA premier mandatory event, will move to number seven in the world rankings with the victory.
The Sydney-born 25-year-old, who beat Venus Williams in the semis, began superbly, breaking to love in the opening game before Wozniacki swiftly broke back to level at 2-2.
After another break each, the Briton took advantage of two double-faults from the Dane to break to 5-4 and serve out for the set.
There was a similar pattern to the start of the second set, with the pair exchanging breaks in the first two game. The key moment came when Konta broke to go 4-3 up, with a little help from the net cord.
No British woman had ever won a premier mandatory event since the elite tier was introduced in 2009 and this was only the second time that Konta had even qualified for the Miami tournament.
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The Briton said her quick start had really helped her in what was just her second premier mandatory final, following her loss to Agnieszka Radwanska in Beijing in 2016.
Konta conceded that there was little to choose between herself and her Danish opponent, who she also beat in the Australian Open in January.
"Until the end there wasn't too much in it. I tried to not wish time away and to really stay out there as long as possible and really enjoy competing. I think even when it was finished I was expecting more points to come," she said.
"I was hoping it was going to be third time lucky in my third final but we will go for the fourth one," said Wozniacki, who nonetheless said she was pleased with the consistency she has shown in the first quarter of the season.
"I think I can take a lot out of this first part of year in general. I think I can take a lot of positives from that and just build on it.
"That's what I'm going to do. I'm going to learn from the things that I can do better, but at the same time not beat myself up too much and just keep working and doing what I'm doing.
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