The tricky winger made all three goals from set piece executions and despite the Cottagers registering twice, it was the home side that took the points.
Fernando Forestieri gave the Owls an early lead before Jamie O’Hara promptly struck for Fulham.
Tom Lees put Wednesday back in the driving seat in the first half and Michael Turner made it 3-1 just after the resumption.
Tom Cairney made the hosts sweat by pulling a goal back midway through the second period but the Owls held on to secure a welcome win.
After a touching minute’s applause for the late Ron Springett, Wednesday almost posted the perfect start.
A deep Wallace fell square on the head of Barry Bannan, whose firm header was acrobatically tipped over by Andy Lonergan.
New recruit Bannan – one of four home debutants – then placed narrowly wide as Wednesday asked certainly asked more of the questions.
And it was fellow new-boy Forestieri who went one better and opened the scoring on 13 minutes.
Wallace delivered the perfect corner and the Italian leapt above his marker to nod into an empty net.
The Owls were well on top and dominated possession before Fulham began to cause problems, with Tim Ream blazing over on the angle from 12 yards.
Ryan Tunnicliffe went closer with a long ranger and the Cottagers continued to press, reaping the reward on 23 minutes.
A loose clearance landed in the path of O’Hara just outside the penalty area and his speculative half volley nestled into the far corner to equalise.
But the leveller served only to galvanise Wednesday, who turned up the heat, with Wallace at the heart of the action.
First the wideman sent a delicious cross in the mix that Alex Lopez headed goalwards but Lonergan pulled off a stunning reflex save.
From the resulting corner, however, the keeper was powerless as Wallace’s pinpoint accuracy to the back stick led to Lees nodding in his second goal of the season to restore the advantage eight minutes before the break.
And it could have been three on the whistle when Wallace delivered yet again from the right but Atdhe Nuhiu’s effort was inches away from the target.
Forestieri made way for Lucas Joao at half time but it was defender Turner who rose to the fore on 49 minutes.
Dangerman Wallace sent another set piece right on the money and the towering loanee powered a driving header in off the underside of the crossbar.
But any hopes the Owls had of cruising home were dashed on 67 minutes when Fulham reduced the arrears.
O’Hara crossed from the right and Cairney ghosted in to head past Keiren Westwood from inside the six-yard box.
The next goal was always going to be key and both sides went after it - Bannan smashed into the side netting after skilfully evading O’Hara and the industrious Kieran Lee was a whisker away from going one on one with Lonergan.
Westwood denied Dan Burn at the other end but despite the best efforts of both sides’ attacks, the defences held firm and the referee called time on an entertaining encounter that the Owls deservedly won.
Wednesday: Westwood, Turner, Nuhiu (Helan 81), Lees, Lee, Lopez, Hunt, Wallace, Pudil, Bannan, Forestieri (Joao 46)