Ameobi struck in front of a crowd of 43,904 after just 15 minutes, although Newcastle were unable to find a second goal and it took good saves by Steve Harper from former Sunderland full-back Michael Gray and substitute Francis Jeffers to ensure all three points stayed on Tyneside.
It was the first time Sheffield Wednesday had been to St James' Park since their ill-fated visit in September 1999, when Sir Bobby Robson's first home game as Magpies manager ended in a thumping 8-0 victory over the Owls.
But much has changed at St James' Park during the intervening decade and all that mattered tonight was a win however it came.
Hughton handed loan signing Danny Simpson a debut at right-back as Ryan Taylor moved into midfield to replace the injured Joey Barton.
Kevin Nolan whistled a 25-yard drive just wide with little more than 20 seconds on the clock as Newcastle made a lively start.
It was they who took the lead with 15 minutes gone when Andy Carroll helped on Harper's clearance and Ameobi controlled before half-volleying superbly inside keeper Lee Grant's left post.
Grant did keep out Ameobi's 28th-minute header from a Ryan Taylor corner, and although Owls striker Jermaine Johnson repeatedly caused problems for Fabricio Coloccini - he set up James O'Connor for a shot which Nolan had to block four minutes before the break - the home side largely held sway before the break.
Ryan Taylor almost wrapped up the win within seven minutes of the restart when, after Sean McAllister had been penalised for a foul on Jonas Gutierrez 25 yards out, he forced Grant into a fine save with a curling free-kick.
Nolan blasted a long-range effort just over after the visitors failed to clear the resulting corner, and it seemed only a matter of time before the home side extended their lead.
But Wednesday rallied as the game passed the hour mark and Harper was called upon to make his first save of the game from Gray's 64th-minute free-kick.
Ryan Taylor could not hit the target after being set up by substitute Xisco and Ameobi 20 minutes from time.
But Harper had to dive bravely at Jeffers' feet with four minutes remaining after full-back Tommy Spurr had played the striker in behind the home defence.