Wilson - a bronze medallist in the team event at the London 2012 Paralympics - was forced to come from behind after losing the first set, but he took the next three in a row to clinch victory from the best-of-five contest.
Daybell looked on course for the victory after the opening set as he took it 11-7, with Wilson losing five points on his own serve en route to the defeat.
Game two proved to be a turning point in the match, though, with the contest swinging both ways before Wilson finally took it 12-10 to level things up.
The victory appeared to give Wilson the lift he needed, and he raced through the third set 11-3 to move one away from the gold medal.
Daybell put up a better fight in the fourth set, but a run of six points in a row - and nine points won on his own serve - helped Wilson over the line with an 11-7 triumph.
Daybell was forced to settle for silver, completing an all-British podium after Joshua Stacey of Wales had earlier won bronze.