Conners, ranked 196th in the world, compiled a crazy, rollercoaster six-under-par 66 that included 10 birdies in the final round at TPC San Antonio.
He followed four early birdies with four consecutive bogeys on the front nine before storming home with six birdies and three pars to claim his first PGA title.
“Definitely a dream come true. It was an amazing day,” Conners told PGA Tour Radio after finishing at 20-under 268 to secure his second shot at the Masters after playing as an amateur in 2015.
WATCH: The Masters – Corey Conners talks about tough first day Augusta National
The 27-year-old from Listowel, Ont., was so low on the pecking order that he was not even exempt into the Texas Open.
Instead, he had to run the gauntlet of a Monday qualifier, among 73 players competing for four spots.
Six players ended up in a playoff for the final berth, and Conners was the man to emerge triumphant.
Hoffman birdied the par-five 18th to shoot 67 and claim second place, a shot ahead of fellow American Ryan Moore (64).
South Korean overnight leader Kim Si-woo (72) faded to equal fourth with American Brian Stuard (66) on 15-under.
Conners started the day a shot behind Kim, but powered to a four-shot lead after just five holes as the birdies flowed.
But what the golfing gods give, they also take away, and the Canadian lost those four strokes as quickly as he had gained them as Hoffman took the lead with a birdie at the ninth.
Although Hoffman did not drop a shot on the back nine and picked up three more birdies, it that was not enough to stop a rampant Conners, whose putter was running hotter than a Texas summer.
He came to the last with a three-shot lead and held his nerve to book the final seat on the Sunday night charter flight to Augusta, where the first major championship of the year will tee off on Thursday.