The midfielder's curling right-footed shot from 25 yards sealed Hull's immediate return to the Premier League.
Steve Bruce's side dominated what was a tense affair at times, with Diame striking a post in the first half.
The Owls struggled to impose themselves as their 16-year exile from the top flight was prolonged.
They had a late handball shout turned down when Jeremy Helan's stoppage-time shot appeared to be blocked by Michael Dawson's arms.
Senegal midfielder Diame's 10th goal of the season was his most important to date in a Hull shirt, with promotion to the Premier League estimated to be worth at least £170m.
The 28-year-old's moment of magic came when he ran on to Robert Snodgrass' lay-off and spotted the opportunity to curl in to the roof of the net past the outstretched fingers of Keiren Westwood in the Wednesday goal.
Victory in a third Wembley appearance in three seasons meant Hull joined champions Burnley in bouncing back to the Premier League at the first attempt, 370 days after they were relegated from the top division.