Megson, who was a fans' favourite during his playing days at Wednesday, has endured a difficult start to life in the City hotseat but a Gareth McAuley header and an Akpo Sodje own goal in the opening 13 minutes gave the Foxes a first away victory in the league to pile the pressure on Owls boss Brian Laws.
Both goals came courtesy of right-wing corners, with Wednesday having no answer to Alan Sheehan's dangerous left-foot delivery.
Laws made three changes to the side that was beaten by leaders Watford in midweek.
Lee Grant recovered from illness to take over from Robert Burch in goal, skipper Lee Bullen replaced the injured Frank Simek and Dutch winger Etienne Esajas came in for the suspended Jermaine Johnson.
For Leicester Sheehan and Shaun Newton came in for Radostin Kishishev and Joe Mattock.
The Foxes had been struggling for goals in recent weeks but they were gifted two inside the opening 13 minutes as Wednesday failed to deal with Sheehan's inviting corners.
First, McAuley took advantage of a static Owls defence to nod home at the back post just six minutes in.
And seven minutes later Sheehan swung a corner in to the near post which Grant failed to deal with, palming the ball against Sodje who could only watch on as the ball rebounded into the corner of the net.
Steve Watson almost pulled a goal back with the interval looming but after a scramble in the box, his goalbound strike was deflected away for a corner.
And to add to Laws' woes, on-loan defender Michael Johnson was withdrawn after sustaining an injury just before the break.
Leicester's central defensive trio looked solid throughout the first half but they were almost caught out three minutes after the break when Deon Burton fired into the side netting.
Wednesday substitute Mark Beevers lifted the home supporters with a perfectly-timed last-ditch tackle to deny Newton a clear run on goal 10 minutes after the break.
Laws brought on summer signing Francis Jeffers and Burton O'Brien with half an hour remaining in a bid to freshen things up.
But Megson has turned the Foxes into a well-drilled defensive unit and they were in no mood to be charitable against a Wednesday outfit that looked devoid of ideas in the final third.
Newton should have put the Owls out of sight when he volleyed Sheehan's pinpoint cross over the bar from cross range at the back post.
And on-loan Leicester keeper Marton Fulop was finally forced into a save with 13 minutes remaining, diving full length to tip O'Brien's right-foot strike around the post.
As Wednesday pushed forward substitute DJ Campbell almost grabbed a third but fired into the Kop after turning his marker.
And Fulop denied Marcus Tudgay in stoppage time, but it was not to be Wednesday's day.
A chorus of boos echoed around Hillsborough at the final whistle as the pressure builds on Laws.
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