Boro dominated for long spells but fell behind when Michail Antonio stabbed home from a corner.
The home side levelled quickly after the break through Mustapha Carayol but despite creating plenty of chances they could not force a winner.
Boro had the first real chance on eight minutes as midfielders Jozsef Varga and Albert Adomah got tangled but the loose ball rolled kindly for Lukas Jutkiewicz to crack in a low 20-yard drive that flew just wide.
Then George Friend played a neat one-two with Carayol to burst down the left then cut into the box to fire an angled 12-yard effort just over.
Middlesbrough's pressure continued as Grant Leadbitter had a low 20-yard effort scrambled behind the foot of the left-hand post then Adomah curled a free-kick wide of the right post.
Wednesday scored the opener on 34 minutes though when a corner was nodded down into a crowd for Antonio to hook home from six yards out.
Tony Mowbray's men were back on the attack as Friend squared for Leadbitter to drill in a low shot that brought a good save.
But Wednesday could have had a second on the stroke of half-time as Jermaine Johnson cut into the box from the right and cut the ball back to Liam Palmer, but the outstretched foot of Jonathan Woodgate turned the shot behind.
Boro levelled quickly after the break. Jutkiewicz got into the box and squared through a static defence for Carayol to stab home from six yards on 49 minutes.
The hosts threatened again on 56 minutes as Adomah touched on a Varga ball for Friend to again go weaving into the box but his eight-yard angled shot under pressure screwed wide. Two minutes Boro went closer still as Jutkiewcz broke into the box onto a Leadbitter ball to hammer against the crossbar.
A low Leadbitter free-kick took a deflection of the wall in the 64th minute and went spinning towards the far post but the goalkeeper scrambled across to save.
Boro went close in the 76th minute as a ball sailed over the box for Andy Halliday on the right. He rode a challenge and forced his way past Johnson to drill an angled shot that the goalkeeper came out quickly to charge down.
Eight minutes from time Adomah collected a Jutkiewicz header down and fired into the side netting and the hosts threatened again as a Leadbitter free-kick bounced through the box for Halliday, unmarked at the far post, but his downward header bounced up and over the crossbar.
Wednesday threatened in stoppage time as Antonio beat the offside flag and broke free into the box, but goalkeeper Jason Steele did well to save his tired low shot.