Wednesday led twice on the day, with Sam Baldock twice levelling for the visitors as Miguel Llera and Gary Madine put them ahead.
And Albert Adomah added a late third to Baldock’s goals, meaning Wednesday lie second-bottom while City move to 21st.
Near the top of the league, the teams chasing leaders Cardiff City failed to close the gap after suffering draws and defeats.
Second-placed Crystal Palace were held to a 2-2 draw at home to Blackpool, while Leicester were also held by that scoreline by visiting Barnsley, who move into the drop zone despite a creditable result.
Middlesbrough moved third after a 3-2 win at bottom club Peterborough, while Hull City went fourth with a 2-1 win at Watford, who stay sixth.
Ipswich’s resurgence under Mick McCarthy continued with a 3-0 win at home to Millwall, the Tractor Boys staying 20th but now five points clear of the drop zone.
Nottingham Forest beat Burnley 2-0, while Huddersfield and Bolton drew 2-2.