The Owls were within a minute of being left frustrated by local rivals Rotherham, who conceded a last-minute penalty slotted in by Steven Fletcher to leave S6 with nothing to show from a resolute performance.
Richard Wood saw red for a late foul on Lucas Joao, the spot-kick was expertly dispatched by Fletcher and Wednesday were rewarded right at the last.
It was a blanket of yellow behind the ball and the hosts struggled to find a way through despite controlling the game from the first whistle to the last.
As expected, the lion’s share of pressure came from Wednesday, with the Millers relying on occasional counters upfield.
The tactic almost paid dividends in the first half as Wood was a whisker away from converting a close ranger header 20 minutes in.
Almen Abdi, making a rare start, then suffered a blow when injury forced the midfielder out of the action.
It might have got worse for Wednesday just before the interval as Wood had the ball in the net but the strike was ruled out for an infringement.
The Owls went close themselves ten minutes into the second half when Lucas Joao clipped over goalkeeper Lewis Price but Darrell Fisher hooked off the line to keep the score goalless.
Joe Mattock almost put through his own goal just past the hour but Price went down low to spare the defender’s blushes before the Millers’ custodian saved a snapshot from Joao.
Steven Fletcher was also denied in the closing stages by Price before Joao was felled in the box and the referee pointed to the spot.
Fletcher stepped up to do the necessaries after Wood was sent off and Fletcher stepped up to decide the derby and send the Owls back into the top six.
Wednesday: Westwood, Palmer, Loovens, Lees, Pudil (Nuhiu 61), Hutchinson, Lee (Jones 46), Abdi (Wallace 34), Reach, Fletcher, Joao