Two moments of magic gave the Owls three vital points at Millwall.
Anthony Musaba delightfully set up Iké Ugbo to give Wednesday the lead before Musaba himself bagged a second from Barry Bannan’s superb through-ball.
Victory for the visitors drags the Lions further into trouble and dims the daylight between Wednesday and the safety line.
And it was no more than the Owls deserved as the performance was measured and controlled once the deadlock was broken.
Ugbo’s goal on 32 minutes illuminated what prior to that was a dull, cagey affair, as was widely predicted given the stakes.
Musaba, picking up possession just past halfway, did ever so well to slip two challenges before delivering an accurate low feed for Ugbo to finish from close range.
That gave Wednesday an injection of confidence and three minutes before half time it was 2-0.
Bannan expertly played in Musaba down the side of the box with a trademark pass and the Dutchman stroked calmly across Matija Sarkic into the far corner.
Millwall had little choice but to chase the game in the second half but with little success.
Zian Flemming had a whistling drive deflected wide and Duncan Watmore was denied on the line by Di’Shon Bernard.
Ryan Longman sent an inviting low cross right into the danger zone, where two blue shirts were inches away from contact, which summed up a barren afternoon for the out of form hosts.
For Wednesday’s part, there was a downside in stoppage time when substitute Ashley Fletcher was sent off after two yellow cards in quick succession.
But in the overall analysis, the win was as welcome as it was necessary and with the gap between the two strugglers trimmed to four points, it’s game on for Danny Röhl's men.
Wednesday: Beadle, Valentin, Palmer, Ihiekwe, Bernard, Johnson, Vaulks (B Diaby 78), Bannan (Fletcher 78), Poveda (M Diaby 77), Musaba (Gassama 61), Ugbo (Smith 67)