Entering the final round of the Valero Texas Open at 14 under and one shot behind overnight leader Si Woo Kim, Connors lept out of the blocks in stunning fashion.
He made 4 birdies in his first 5 holes to lead by 4 from a struggling Kim and American Charley Hoffman.
But inexplicably, Connors immediately followed his scorching start with 4 bogeys in sucession to make the turn one shot behind Hoffman.
And Connors' scorecard got even crazier, bookending his bogey-train with a hat-trick of birdies from the 10th to re-emerge as the leader.
If par avoidance was a statistic, the 27-year-old would be in a league of his own with just one of them through 12 holes.
Meanwhile, American Ryan Moore, playing three groups ahead, birdied the short 16th to surge into a tie for the lead with Connors at 17 under.
Hoffman too reached 17 under with a birdie at the par-5 14th but his effort was matched by Connors who returned to 18 under and wasn't done yet.
Birdies at 16 and 17 took his Sunday birdie tally to 10 and gave him a three-shot cushion over playing partner Hoffman with only the par-5 18th to play.
O Canada! @CoreConn's crazy round ends with a victory.April 7, 2019
A three-shot hole for almost everyone and with a creek weaving its way through the lay-up area and right up past the green, the potential for disaster remained but Connors was textbook in his approach.
A safe lay-up and cautious third shot to the back left corner of the green, well away from the water, was followed by a long-range two-putt to finish at 20 under and two clear of Hoffman.
Moore was alone in third at 17 under while Kim's even par 72 left him sharing fourth at 15 under with American Brian Stuard.
Not only was it Connors' first PGA Tour win but his first victory on any significant tour and paves the way for his first US Masters appearance as a pro.
Aaron Baddeley and Matt Jones were the only Australians to play the final round and shared 30th at 7 under.
Want video tips delivered straight to your inbox? Subscribe to iseekgolf.com newsletters.