Hull City were the more dominant in opening 45 minutes with excellent chances from Tom Huddlestone, Abel Hernandez, Diame and Moses Odubajo but all failed to beat a inform Kieren Westwood.
The second period became a much more open affair with Fernando Forestieri and Michael Dawson having good opportunities early on but both failed to open the scoring. However, Diame had the final say as his excellent strike secured Hull's passage back into the English top-flight.
It only took three minutes in the richest game in world football to produce the first opportunity and it came from Steve Bruce's side as Huddlestone attempted a shot from distance which proved too hot to handle for Westwood initially, but he did well at the second time of asking.
It was then the turn of Carlos Carvalhal's side, who were appearing at the national stadium for the first time since 1993. Ross Wallace looked to make it a happy return with his curling free-kick in the 15th minute, though stand-in Edlin Jakupovic did well to punch it clear.
Turning the screw
The Tigers began to dominate as the half went on and had some excellent chances to open the scoring.
They came within inches of taking the crucial lead when a corner in found the head of Hernandez but luckily Tom Lees was on the line for Wednesday to chest away the effort. He was handed another great opportunity moments later when a ball from Diame deflected through to the Uruguayan, only for Westwood to come flying off his line to deflect the toe poke over.
Diame had his own opportunity seven minutes before the break as he managed to wriggle his way past three Wednesday defenders on the edge of the area and cannoned a shot towards goal which would have given Westwood no chance; it clattered off the post, however.
Both sides came flying out of the traps in the second period and both had good chances to open the scoring in the opening exchanges.
Dawson was caught out by a long punt upfield which allowed Forestieri to run in on goal but luckily for the former Tottenham man his defensive partner Curtis Davies was on hand to get across and clear the danger.
Dawson looked to make up for his error as a Robert Snodgrass corner fell at his feet in the 52nd minute, though Westwood was there to rush out and block the effort.
The best chance of the gam up to that point fell to Bruce's side just before the hour mark as Odubajo played a perfect ball into the area and it seemed an easy opportunity for Robertson but he somehow managed to send the effort well over the crossbar.
The contest at Wembley seemed to be edging towards extra-time that was until the 71st minute as Hull managed to open the scoring.
It was a perfect way to secure their return to the Premier League as the ball made it's way to Diame who took a touch outside the area before curling his effort which just couldn't be kept out by Westwood and sent the 30,000 plus Hull fans into dreamland.