Rotherham posted a precious 1-0 win at Hillsborough and dented the Owls’ impressive home record along the way.
Matt Derbyshire’s goal was the difference as Wednesday suffered only their second defeat in S6 of the season.
Despite dominating almost all of the possession thereafter, particularly in the second 45, the Owls couldn’t break down a stern Millers backline – although the hosts remain in the coveted top six.
Before the visitors netted their decisive goal, Wednesday had a let-off inside two minutes when Grant Ward took a neat feed from Matt Derbyshire into his stride and his sweet half volley whistled wide.
The Millers were undeterred, though, and did register on 21 minutes.
Lee Frecklington delivered a telling feed right into the corridor and Derbyshire was left with a simple tap-in at the back post.
Wednesday went on to pose more questions in the first half and thought they had levelled ten minutes before the break.
Some outrageous skill from Aiden McGeady took the Everton loanee into the penalty area on the angle, where his shot was deflected into the net by Michael Turner.
But just as the Owls were celebrating what they thought was an equaliser, the strike was chalked off after consultation between the officials deemed Turner to be in an offside position.
Both sides then had quick-fire chances to score – Danny Ward slotted wide from a Grant Ward cross before Jack Hunt unleashed a fierce drive that flew inches past the upright.
Wednesday went closer still five minutes into the second period when Ross Wallace struck a curler from 20 yards that smashed against the crossbar.
Then on the hour, the Owls again had the ball in the net – this time through Gary Hooper – only for the linesman’s flag to intervene once more.
It was one-way traffic and substitute Lucas Joao advanced on goal to force Lee Camp into a diving save.
The Rotherham keeper denied Wallace from a set piece 15 minutes from time as the Millers clung on to their slender advantage and despite staying on the back foot, the earlier damage was done and the visitors made the short hop back across South Yorkshire with the points.
Wednesday: Westwood, Hunt (McGugan 74), Turner, Lees, Pudil, Wallace, Bannan, Lee, McGeady (Joao 46), Nuhiu, Hooper