The first half was an evenly contested affair, with both sides battling for control in the early stages. Nauzet was called into action early on, getting down low to keep out a shot from Francis Ferron.
St Joseph's took the lead in the 13th minute when Ferron's effort was deemed to have crossed the line before Christian Rutjens could clear.
The Imps responded by looking to create an opening of their own, with their first real chance coming just before the half-hour mark. Mandi's long-range effort was heading towards the top corner, but Bradley Banda was equal to it and tipped the ball over the bar.
Saints held onto their advantage and went into the break 1-0 ahead.
Juanma Pavon made a triple change at half-time, introducing Manuel Toledano, Alex Mula and Nano, and the changes immediately transformed the game.
The Imps found their equaliser just five minutes after the restart. Kike latched onto a through ball before squaring it across goal, where Toledano got in front of his marker to poke the ball past Banda and make it 1-1.
The momentum was now firmly with the Imps, and the front two linked up perfectly again to complete the turnaround in the 55th minute. Toledano drifted past Javier Paul before finding Kike, who made no mistake from close range to put Lincoln 2-1 ahead.
Just two minutes later, Leon Mason made an immediate impact after coming off the bench, turning provider for Kike. The forward produced a brilliant finish from outside the box, curling his effort into the bottom corner to complete his brace and make it 3-1.
Having turned the game around in a devastating spell after the interval, the Imps managed the remainder of the match expertly, seeing out St Joseph's and securing back-to-back Pepe Reyes Cup triumphs.
The victory provided the perfect response following the disappointing defeat to Larne just a few days earlier, as the Imps lifted another piece of silverware and began the next chapter of the season with a confidence-boosting win.