An 80th-minute goal from a Whitby Town trialist ensured the club won the Mickey Skinner Memorial Trophy for the first time since 2014.
A tight opening 20 minutes eventually brought chances, and it was the visitors who went threatened first.
Steven Snaith's quick free-kick found Luke Bythway in space. His attempt, one-on-one, was blocked at the feet of James Dawson. The loose ball, however, found Weledji, whose curling effort went just over the bar.
The Blues continued to threaten, and could have broken the deadlock, just past the half-hour mark.
Adam Gell found Carson, who drove through the middle and unleashed a ferocious attempt from 25 yards, which whistled just over, similarly to Weledji's effort just ten minutes earlier.
Guisborough had chances, however. Most notably through Steve Roberts.
The Prioryman picked the ball up in the middle of the park, before unleashing a powerful shot, which Bland just parried wide.
After a raft of changes by Whitby at the break, Guisborough continued to look more comfortable.
Just under 20 minutes, Matty Lovatt beat Weledji, before breaking into the box, though he could only fire over the bar.
Despite Whitby's creativity being stifled thanks to a raft of changes, it was them who would open the scoring.
A Blues trialist played a neat one-two with Matty Tymon, before being found in space with only Dawson to beat. He obliged and slotted the ball through the legs of an onrushing Dawson.
Guisborough could have forced a penalty shoot-out with just four minutes remaining, though Tom Bligh could only send his shot into the legs of Shane Bland, leaving Whitby clear to take back the bragging rights from their rivals.