Alan Irvine's side went into the game desperate for a win but they were unable to take anything from the north east as Scott McDonald's deflected first-half goal proved enough for Boro.
The Owls' cause was hampered before play even began as Leon Clarke was unable to take his place in stating line-up after suffering an injury during the warm-up.
The early setback did not deter the Owls, though, and they could have taken an early lead but for a good double save from Brad Jones, denying Darren Potter and Marcus Tudgay.
Spurred on by their early flourish, Wednesday created another opportunity moments later when Jermaine Johnson's acrobatic bicycle kick went just over the crossbar.
The barrage of pressure continued and Potter again nearly put the visitors ahead, firing a 25-yard effort wide.
Boro started to come into the game midway through the half, though, and began to fashion opportunities of their own.
Their endeavour left them susceptible to a counter-attack and they should have been behind in the 26th minute. Johnson broke away from the Middlesbrough backline and found himself one on one with the Jones before scuffing his effort straight at the Australian stopper.
Wednesday continued to create chances, though, as Darren Purse saw his header saved, before Tommy Spurr fired an excellent ball across the six-yard box which nobody could get on the end of.
Gordon Strachan's men always looked dangerous when they went forward as former Celtic midfielder Barry Robson forced an excellent save from Lee Grant after good link-up play with McDonald.
The Owls paid the price for their lack of cutting edge in front of goal as Middlesbrough took a fortuitous lead five minutes before half-time. McDonald surged towards the Owls' backline before firing a seemingly innocuous 30-yard strike towards goal only for it to take a huge deflection off Tom Soares, wrong-footing Grant.
Wednesday picked up where they left off after the break but were guilty of gifting the hosts possession with several sloppy passes.
The visitors were certainly showing fight, though, and they twice came close to equalising just after the break. First, the impressive Johnson saw his effort deflected wide, before Luke Varney rattled the crossbar from the resulting corner.
And the Owls were nearly forced to pay for spurning chances again but Grant saved excellently from Rhys Williams.
Irvine brought on Etienne Esajas and Francis Jeffers in a desperate attempt to grab a point and the latter nearly did just that in the 86th minute but was unable to beat Jones.
Boro should have finished the game off moments later but Grant produced an excellent save to deny Leroy Lita from 12 yards. It did not matter though as Strachan's side saw the game out.