The 57-year-old former Southampton and Cardiff boss was relieved of his duties on Sunday following a woeful start to the season that saw the Owls secure only one win.
The 2-0 defeat at Blackpool proved to be the final straw for chairman Milan Mandaric, whose decision to axe Jones failed to get an immediate reaction here as Anthony Knockaert fired the visitors into an early lead.
However, Wednesday - led by first-team coach Stuart Gray - showed the Hillsborough faithful what they were capable of as they ended a run of three straight defeats courtesy of on-loan Sunderland striker Wickham's first-half double.
The home side's workmanlike performance will give Mandaric confidence that this group of players can lift themselves out of the relegation zone under a new manager.
As for Leicester, their first loss in three games saw them surrender their three-point lead at the top, QPR's win over Bournemouth moving them level with Nigel Pearson's side.
The reasons for Wednesday's failure to keep a clean sheet this term were evident as early as the third minute when sloppy defending allowed Knockaert to blast his side ahead. The tricky winger somehow shimmied his way through the backline before unleashing a close-range effort into the roof of the net.
However, the hosts responded in emphatic fashion seven minutes later thanks to Wickham, who controlled a swirling cross, possibly with his hand, at the back post and drove an unstoppable shot into the far corner.
Wickham could have had a second soon after when Giles Coke robbed Wes Morgan in the middle of the field and played in the England Under-21 forward, but his fierce effort was parried away by Kasper Schmeichel.
After Lloyd Dyer fired hopelessly over the top following a superb Paul Konchesky through-ball, Wickham netted a resurgent Wednesday's second in the 24th minute.
The ball squirted out to the 20-year-old, in a similar position to his first strike, and his intended cross caught a static Schmeichel cold, with the ball flying into the bottom corner.
Jamie Vardy missed a glorious opportunity to level things up 10 minutes before the interval, the former Fleetwood striker failing to connect cleanly with a long ball over the top that bounced into the arms of a grateful Damian Martinez.
Morgan and David Nugent volleyed wide either side of half-time as Leicester pushed for an equaliser.
Leicester were starting to dominate and Martinez produced a stunning save to palm Nugent's cushioned half-volley from the edge of the box round the post, while Vardy was off target following some neat control from a long ball.
Gray's side struggled to keep possession in the final 20 minutes but Wickham almost grabbed his hat-trick, only for Schmeichel to produce a stunning save.