Prior to Wickham's goal, the main talking points had been a red card for each side and Scunthorpe's spoiling tactics which saw them waste time at every opportunity, earning them the wrath of the home fans.
Town could have scored in the opening minute when Jon Walters raced onto a long ball but he fired narrowly over and the home skipper also fired wide after good work by Pablo Counago and Daryl Murphy.
Scunthorpe were happy to hit on the counter-attack, but they should have scored on 23 minutes when Paul Hayes led a swift breakaway and found Matt Sparrow in space but Brian Murphy made a good save to beat away his shot.
Walters failed to connect cleanly with a great chance from a superb Owen Garvan free-kick and then Counago felt he should have had a penalty as David Mirfin clambered all over him as they contested Shane O'Connor's cross.
Joe Murphy denied namesake Daryl and Counago with simple saves but then made a better one to deny a curling Counago effort which appeared destined for the top corner.
Both teams could have scored within 60 seconds close to half-time as first Counago nodded against the bar for Town and then Hayes' 18-yard volley brought a fine tip-over save from Brian Murphy.
Sparrow shot narrowly wide for Scunthorpe in the first chance of the second half, before Joe Murphy arched to tip over a Walters header from Garvan's cross and then Gareth McAuley headed the ensuing Garvan corner wide.
A firm McAuley header from another Garvan corner was blocked, Mirfin blocked a Counago shot and Joe Murphy fielded a 25-yarder from O'Connor as Town turned up the pressure.
Hopes of a home win were increased on 69 minutes when Iron captain Cliff Byrne was sent off by referee Pat Miller for blocking Jack Colback's forward run with a raised arm.
David Norris directed a free header wide from an O'Connor cross before Town were also reduced to ten men when Damien Delaney harshly saw red for a foul on sub Jonathan Forte just inside the home half, even though McAuley was also back.
Ipswich continued to threaten though with sub Carlos Edwards drilling a low ball across the six-yard box which Joe Murphy parried and Sam Togwell hooked clear before fellow replacement David Healy volleyed over.
The game looked destined to end in a stalemate until Wickham, who doesn't turn 17 until the end of the month, brought down a long ball, turned his man and coolly slotted home in the second added minute.