Michail Antonio’s early strike was enough to separate the sides and on the balance of play, the Yorkshiremen probably merited their win, recorded in front of 16,248 people.
Gers did improve considerably after the interval though and had good chances to secure a draw which will have encouraged Ally McCoist.
Overall, it was another good workout against a decent Owls side which will bid to win promotion to the Premiership in the months ahead.
Now attentions turn to the real thing, with 2013/14 due to start this Sunday against Albion Rovers in the Ramsdens Cup.
On the face of it, this result might not add a lot of weight to the suggestion but Gers are certainly ready to play competitive football.
That absolutely wasn’t the case 12 months ago and McCoist’s men are in infinitely better shape than they were going into last term.
Wins in five other friendlies – including two against good Bristol City and Emmen sides – have made for a very worthwhile preparatory period indeed.
The manager’s team selection here was notable, with the starting XI likely to be along the lines of the side which will face the Coatbridge team at Almondvale.
With only two trialists permitted to play in that tie, it was Nicky Law and Jon Daly who occupied those spots against Wednesday.
Captain Lee McCulloch moved back to central defence beside Emilson Cribari, while Scott Gallacher started in goals ahead of Cammy Bell.
It was the hosts who made the more enterprising start, with Gary Madine heading Jeremy Helan’s right-wing cross just past the post.
Jermaine Johnson also hit the target with a firmly-struck drive but Gallacher got down well to hold it.
Gers offered little in return against their most able opponents of the summer campaign, with their final pass often letting them down.
And it was no surprise when Wednesday took the lead after 11 minutes, with the impressive Antonio putting his team ahead.
The former Reading player’s finish was far from emphatic but an awkward half volley into the ground from Joe Mattock’s corner was enough to beat Gallacher as it spun up into the net.
Falling behind prompted an increase in tempo of sorts from Rangers after they had struggled to get to grips with a potent home front line.
Andy Little had a shot closed down, Kamil Zayatte had to react well twice to clear with strong headers and Lewis Macleod very nearly picked out Daly in a threatening area.
Although the Third Division champions didn’t always look dangerous when they came upfield, they did settle a little more and hung in.
As they tried to drag themselves back into the game, what was happening on the terraces was quite often of more interest.
A vocal, exuberant away support of around 5,000 had travelled south in good spirits and created a terrific atmosphere in Sheffield before kick-off.
That carried on to the game itself, with locals impressed by the way they backed their team to the point they co-ordinated their own singing around what came from the away end.
A Union Flag bearing the words ‘Drummer Lee Rigby Lest We Forget’ in tribute to the killed soldier was also passed from Gers fans to home followers to great applause.
And with the behaviour of those in the Leppings Lane Stand of a great nature, they could unquestionably go home holding their heads high at their conduct.
Back on the pitch, boss McCoist resisted the temptation to make changes during the break for the start of the second period.
Keeping faith paid off as the match became a more even contest initially before the Light Blues enjoyed a good spell of sustained pressure.
Prior to that, Johnson drew a good stop from Gallacher at one end then Law dragged a shot wide at the other in response after being released by Macleod.
As time went on, Rangers grew in confidence and Little forced replacement keeper Adam Davies into a smart stop.
The Northern Ireland star then beat the Wednesday goalie with a rapid shot on the turn but it flew agonisingly past the post too.
Substitute Nicky Clark also diverted wide when he should really have bulged the net within moments of coming on.
But the most glaring miss of the night came from Bilel Mohsni, who somehow put the ball over an open goal when Davies spilled a wicked Macleod rocket from 30 yards.
Time was beginning to get the better of Rangers and as Daly’s header was held, it became apparent this wouldn’t be their night.
So it proved, with Antonio’s first-half counter doing enough damage to condemn McCoist’s team to a first pre-season defeat.
That won’t bother him though and he’ll take heart from the way his players held their own. Now Rovers are in his sights and that game can’t come quickly enough.
RANGERS: Gallacher; Faure, McCulloch (Mohsni 62), Cribari (Clark 62), Wallace (Peralta 72); Black; McAusland (Smith 72), Macleod (Crawford 72), Law; Daly, Little (Foster 62).
SUBS NOT USED: Bell, Gasparotto, Aird.
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