The hosts edged the balance of play in the first half, but visiting keeper Sam Slocombe was on hand to save headers from Ryan Leonard and Freddy Eastwood.
After the break, Shrimpers defender Ben Coker mistimed a header into the path of Iwelumo, who nodded the Iron ahead.
Kevan Hurst came closest to an equaliser with an effort that Slocombe tipped over, but Scunthorpe held on.
Scunthorpe, who looked much the better side after Iwelumo's effort, could have extended their lead when Eddie Nolan's header went just over and Sean McAllister's long-range strike forced a superb save from Daniel Bentley.
Phil Brown's Southend have now lost their last four matches.