Diame broke the deadlock with a magic long-ranger after being teed up by Robert Snodgrass to crown an outstanding personal performance.
Try as they might, Wednesday, backed by a magnficent travelling army, couldn’t find a way back in and lacked a spark in the second period when Hull were on top - with their exile from the top-flight continuing.
It was fitting that the golden moment arrived from Diame, who crashed an effort against the post in the first period and was the game’s stand-out player.
A wall of noise greeted both sides with the 41,000 strong Wednesday contingent being particularly voiciferous on the club’s first visit to the home of football in 23 years.
Hull, unchanged from the side who edged home in their play-off semi-final second leg with Derby, had the game’s first opening when Jake Livermore teed up Tom Huddlestone, whose drilled shot was held comfortably by Kieren Westwood in the fourth minute.
A good spell of pressure then saw the Owls exert themselves with Michael Dawson felled for a late challenge after bringing down Fernando Forestieri down the left channel as the Owls talisman announced himself on proceedings in the tenth minute.
Forestieri’s effort was punched away by Jakupovic, not entirely convincingly, and the Swiss international was then called upon in the 16th minute after Wednesday earned another dangerous free-kick opportunity after Mo Diame brought down the recalled Sam Hutchinson, brought into the side in place of Alex Lopez.
Ross Wallace’s curler was beaten away by Jakupovic, with Wednesday starting to have the better of it and gain the upper hand.
After a quiet opening half-hour, Hull wrestled the momentum back and went agonisingly close to taking the lead on three occasions in a powerhouse
A corner was needlessly conceded by Westwood, with Robert Snodgrass’s outswinger finding the unmarked Abel Hernandez, whose goalbound downward header was blocked on the line by Kieran Lee, with the Owls midfielder then diverting Michael Dawson’s bundled follow-up, with appeals for handball rebuffed by West Yorkshire referee Bobby Madley.
Ahmed Elmohamady then miscontrolled when sent clear on goal by Diame, who sent Hernandez clear soon after, with Westwood racing out and making a fantastic save to divert his goalbound strike.
Moses Odubajo then saw a drive whistle just wide before excellent play by Diame saw home forge a chance on the left, with his fierce strike thumping the post with Westwood beaten after he showed nifty footwork to weave his way into the area.
Odubajo was soon almost afforded a sight of goal on the left, but his control let him down and Westwood blocked with the half ending with Tom Lees seeing his header held by Jakupovic.
The first action of the second period saw Curtis Davies show his mettle to produce a timely challenge to deny Forestieri from getting in a strike on goal after being sent clear as Wednesday sought a response in front of their huge contingent of fans after being pinned back in the final 15 minutes of the first half.
At the other end, Westwood, having a sound game, then produced another telling contribution, racing out to block Dawson’s shot after Snodgrass’s left-wing cross found its way to him on 52 minutes.
Hull then spurned a golden opportunity five minutes later as the chances started to stack up, with Andrew Robertson somehow contriving to fire over from six yards out in front of a gaping goal after an excellent low cross from Odubajo.
Aided by the reprieve, the Owls soon fashioned a decent chance of their own when Hutchinson saw his twenty-yarder fly over after a surging run.
The breakthrough finally arrived 18 minutes from time and it proved the sweetest of moments for Diame.
Lees poor clearance was picked up by Snodgrass, who played the ball to Diame who let fly with a sublime 25-yarder which arrowed into the top corner and despite Westwood getting a hand to the strike, he couldn’t keep it out in the game-breaking moment.
A fine challenge from Glenn Loovens denied Hernandez a second and despite having plenty of the ball, the Owls couldn’t create the chance they craved.
Their most threatening moment arrived in stoppage-time, with Madley unmoved when a shot struck Dawson, with appeals from handball rebuffed.
Hull City: Jakupovic; Odubajo, Dawson, Davies, Robertson; Snodgrass (Clucas 82), Huddlestone, Livermore, Elmohamady; Diame (Maguire 89), Hernandez (Meyler 85). Substitutes unused: Kuciak, Bruce, Maloney, Akpom.
Sheffield Wednesday: Westwood; Hunt, Loovens, Lees, Pudil (Joao 86); Hutchinson (Nuhiu 76); Wallace (Helan 63), Lee, Bannan, Wallace, Hooper, Forestieri. Substitutes unused: Wildsmith, Sasso, Lopez, Matias.
Referee: B Madley (West Yorkshire).