The Owls followed their 3-2 success at the Riverside, with goals from Atdhe Nuhiu and Will Keane reward for an improved second-half display.
Keiran Westwood returned in goal after a one-match ban as Stuart Gray kept faith with the side who beat Millwall in midweek.
There were few chances in the opening 45 minutes.
Albert Adomah claimed for a penalty early on after going down near Claude Dielna.
But the appeals were waved away by referee Stephen Martin, while Adam Forshaw fired wide.
Keane headed over for Wednesday, after a good knockback from Nuhiu, before left-back Dielna had the first serious shot on target which Dimitrious Konstantopoulos saved comfortably.
After the break, the Owls stepped up a gear and netted twice.
Nuhiu converted a penalty after handball in the box, before a Lewis McGugan free-kick found its way on to the post, looked like Nuhiu got a touch, before Keane reacted quickest to net.
Boro - who were unhappy with Jose Semedo after a second-half incident with Grant Leadbitter - rarely tested Westwood, Patrick Bamford going closest with a couple of efforts.
Wednesday head coach Stuart Gray was pleased to see his side claim a first home win since Boxing Day and said his players had worked on nullifying Boro’s threat.
“It’s a long time coming,” Gray said. “We’ve had these watched two or three times now and if you stand off them, they’ll hurt you because they’ve got quality players, they’ll pick out quality passes.
“We worked all week to press and close down and force errors, which we did do. It was an open game in the first half but we probably dominated more with the ball but neither keeper was worked.
“Second half, our performance thoroughly deserved the win.
“The only way they were probably going to get in was on a counter attack. We’ve caused a good side problems by being in their faces and they couldn’t get into any rhythm.
“Every game I’ve seen them, they’ve dominated the games through the midfield and we stopped them from playing and suddenly we were on the front foot.
“We won more second balls today, we became more creative and we caused them problems.
“In our last three games we’ve got seven goals but we’ve achieved nothing and we’ve got to make sure we keep going.”