Stuart Gray’s side kicked off the summer with a routine win over York last Saturday and followed that travelling triumph with another victory against Bury six days later.
Jacques Maghoma sent the visitors into an early lead but Wednesday were pegged back just before half time by Daniel Nardiello.
Then the friendly affair was settled in the second half - firstly by Atdhe Nuhiu on the hour, which was a fitting reward for the striker following an industrious display at The AJ Bell Stadium.
Former Bury loanee Giles Coke put the game out of the Shakers’ reach with a fierce drive in the closing stages to make it 3-1.
Back to the beginning, Wednesday found themselves a goal to the good inside three minutes, which gave them the platform to dominate much of the opening period.
Caolan Lavery picked up possession outside the area and threaded a nice ball through to Maghoma, who slotted home with ease from six yards.
A smart move ten minutes later almost saw the Owls profit again, with Michail Antonio and Nuhiu combining to tee up Kieran Lee but the midfield man shot straight at the goalkeeper.
Wednesday enjoyed more of the ball as the first half unfolded, with Antonio flashing wide from distance before Liam Palmer forced Shwan Jalal into a near post save.
But with the Owls in the driving seat, Bury drew level on 44 minutes.
Jim McNulty swung a dangerous corner into the mix and Nardiello was left with the simple task of tapping in from close range.
Then right on the whistle, Nardiello was only denied a quickfire second by a flying Keiren Westwood stop at his near post.
Westwood gave way to Joe Wildsmith at half time and the youngster was soon called into action, saving smartly when Craig Jones forged a route on goal.
Wednesday hit back with Nuhiu poking narrowly wide before the big man put his name on the scoresheet on 57 minutes.
Antonio delivered an accurate set piece and Nuhiu was up first to direct a glancing header in off the underside of the crossbar.
Bury responded with ex-Owl Ryan Lowe’s free kick brushing the side netting and Nicky Adams might have done better following a corner but spooned over the bar.
But the contest was all but over ten minutes before time when Jeremy Helan burst down the left channel and fed Coke to drill past Jalal and seal victory.
Owls: Westwood (Wildsmith 46), Palmer (Floro 87), Helan (Young 87), Hutchinson (Mattock 46), Loovens (Zayatte 46), Semedo (Coke 42), Antonio, Lee (McCabe 60), Nuhiu (Maguire 71), Lavery (Madine 61), Maghoma (Corry 78)