The Owls sacked Dave Jones on Sunday after just one win in all competitions so far this season but caretaker boss Stuart Gray managed to stop the rot after three consecutive losses.
Anthony Knockaert gave City the lead after just three minutes but Wickham equalised six minutes later and then scored the winner with a shot across goal that could well have been intended as a cross.
QPR moved level with Leicester at the summit thanks to a comfortable 3-0 win over Bournemouth.
Charlie Austin netted his fifth goal in as many games at Loftus Road just before the half hour and Junior Hoilett doubled the lead in the second half.
Substitute Matt Phillips then scored a beauty in the second half after beating three men to seal the win.
Paddy McCourt had the managerless Tykes ahead against Brighton when he embarked on a jinking run and, after playing a neat one-two with Marcus Tudgay, slotted past Tomasz Kuszczak 10 minutes before the break.
It was 2-0 five minutes after the break through Jacob Mellis before a Matt Upson header from a corner halved the deficit but Barnsley - who parted company with David Flitcroft at the weekend and had Micky Mellon in caretaker charge - held on.
There was a dramatic finish at Huish Park as Blackpool had three men sent off at the death in a 1-0 defeat to Yeovil.
John Lundstram scored the only goal after 21 minutes before Kirk Broadfoot was sent off in the 90th minute for a second bookable offence.
Ricardo Fuller was then given his marching orders after an off-the-ball clash before Gary MacKenzie was handed a second yellow card to leave Paul Ince's side with eight men.
Ipswich beat Blackburn 3-1 at Portman Road with Luke Hyam firing the home side ahead after just four minutes but Jordan Rhodes levelled things up for Rovers after half an hour.
Town started the second half in similar fashion to the first with Carlos Edwards regaining the lead in the 48th minute and an error from Blackburn goalkeeper Jake Kean allowed Frank Nouble to score four minutes from time.
There were also four goals at the Den as Millwall drew 2-2 with Nottingham Forest.
Millwall took the lead after eight minutes through Steve Morison but Andy Reid grabbed one back for the visitors eight minutes before the interval.
Martyn Woolford gave the Lions their lead back early in the second half, although it was not to last for long with Nathaniel Chalobah heading home a corner to level things back up.
An emphatic finish from Lee Novak saw Birmingham take a 29th-minute lead against Doncaster but Rovers substitute David Cotterill lashed home a long range effort in a 1-1 draw.
Fourth-placed Reading claimed a 1-0 win over Charlton thanks to Billy Sharp who scored the only goal in the 13th minute to leave the Addicks just two points above the drop zone.
Huddersfield were also 1-0 winners over Bolton as Oliver Norwood hit a stunning 71st-minute strike.