The 19-year-old striker, on loan from Sunderland, crashed home a volley from close range in the second half as Wednesday secured only their second win in their last six league matches.
Wickham, relegated to the role of substitute, stepped off the bench to apply a thumping finish to defender Lewis Buxton’s cross and heap more pressure on Leicester manager Nigel Pearson, whose side’s hopes of a top-two spot have faded in recent weeks.
The Foxes, who needed a stoppage-time header from on-loan Manchester United defender Michael Keane to salvage a point against Leeds in midweek, have now won only one of their last seven league matches.
Keane almost repeated the feat in the 81st minute, but this time his header from substitute Anthony Knockaert’s corner hit the post.
Jeff Schlupp made his first start for Leicester since November at left-back and winger Ben Marshall returned to the side, while on-loan Swansea striker Leroy Lita and defender Reda Johnson were recalled by Wednesday.
Leicester striker David Nugent forced a superb early save from Owls goalkeeper Chris Kirkland with a dipping 20-yard shot and Keane headed Marshall’s corner over the crossbar.
Nugent rifled another effort from outside the area wide before Wednesday responded with their first chance in the 12th minute, Lita flashing a header wide from Michail Antonio’s cross.
But Kirkland was the busier of the two goalkeepers. Marshall fired in a shot from outside the penalty area straight at him and Leicester defender Ritchie De Laet tested him in similar fashion just before half-time.
Marshall provided another telling cross, this time for Harry Kane shortly after the restart, but the on-loan Tottenham forward headed tamely off target.
Leicester goalkeeper Kasper Schmeichel was then forced into a rare save at the other end when Antonio drilled a shot straight at him from inside the area.
Owls defender Johnson had to go off injured and was replaced by Wickham just before the hour mark and Pearson sent on Knockaert for Kane soon after.
Marshall blazed a shot from 12 yards over the crossbar and Leicester were then punished for their missed chances.
Buxton swung the cross over from the right and Wickham crashed the ball into the roof of the net, on the volley, from eight yards.
Keane almost saved the day again in the 81st minute when his header from Knockaert’s corner hit the post.
There was more woe for Leicester in the 86th minute when De Laet was forced off injured and replaced by Sean St Ledger.
Wednesday held on without any further near-misses to send the Foxes spinning to a third defeat in their last five home league matches.
Wednesday manager Dave Jones was delighted to see his side bounce back from the disappointment of defeat against Watford on Tuesday night.
Jones said: “The performance was a follow-on to the other night. I talked to the players about belief and I felt let down by the officials on Tuesday night.
“But I said to the players we have to forget that because this was another big game for us.
“It shows you how far we have come as a football club because when we played them in November they were far the better team and we had some catching up to do.
“I think we were a bit naive earlier in the season in what we were doing and it took us a little time to adapt. We have lost that naivety and become a bit more solid.
“We were getting pulled out of position too much because we were so enthusiastic. So I think it is an all-round thing and the coaches have worked hard.
“Every manager will tell you they have a game plan and we had one. It didn’t work the other night against Watford, although it should have done in all honesty. But today we didn’t switch off at all.
“The centre-halves were magnificent, throwing their bodies on the line, but they all were. This is not the easiest place to come, although I have had joy here in the past. Hopefully the run will continue because the players had to put a shift in today against a very good side.”