Konta, who ousted number three seed Simona Halep in a marathon quarter-final match, also became the first British woman to win a WTA Premier Mandatory event.
The victory meant the 25-year-old moved to a career-high seventh in the world rankings, beating her previous best of ninth last autumn.
Both women were competing in their first Miami Open final, but, while Wozniacki was in search of her first win of the year, Konta had already won the Apia International in Sydney.
Konta got off to the dream start with a break of Wozniacki's serve in the first game of the match and then held her own to take a 2-0 lead with an ace.
The Dane, who was contesting her third final of the year after Doha and Dubai, got into her groove with her next service game to hold, but called over her father for a coaching session just 10 minutes into the match during changeover.
Whatever was said seemed to make a difference as the former world number one hit four points in a row to break back and level at 2-2.
The duo had a closer battle in the fifth, but Konta found her way to break Wozniacki's serve for the second time to edge back ahead before the next two games went with serve.
The Briton still had the upper hand, though, but a fired up Wozniacki, who repeatedly gave determined looks to her box, pushed her repeatedly to advantage on her next service game before claiming a break which levelled the opening set up at 4-4.
Konta hit back quickly though and again broke her opponent before firing in some great serves to clinch the first set.
The Sydney-born player, who made it to the quarter-finals of the event last year on her debut, targeted Wozniacki's forehand to good effect, claiming yet another break in the first game of the second set.
However, the see-saw nature of the final continued, as 26-year-old Wozniacki immediately broke back before holding her own to take a 2-1 lead.
The Dane received attention and had her right foot and ankle strapped in a medical time-out, but continued with the match, which went with serve to see Wozniacki 3-2 ahead in the second.
Konta held her next serve before breaking Wozniacki and holding again to lead 5-3, putting her one game away from the title.
The pressure was all on Wozniacki's service game and Konta moved to championship point with a blistering return before claiming the title after a Hawkeye check on her winning lob.