Phil Brown's side enjoyed more possession and the better chances in the opening hour of the match, but Iwelumo's strike on 64 minutes condemned the Shrimpers to a fourth straight league defeat.
Stand-in captain Freddy Eastwood provided much of Southend's goalscoring threat in the first half, but could not break the deadlock in rainy conditions on the Essex coast.
The former Coventry City striker bent a shot just wide of the far post inside 10 minutes and struck powerfully over the crossbar a short while later.
The experienced forward was gifted a second opportunity to score just after the hour mark, courtesy of a mistake from Southend defender Ben Coker.
On the far side of the area, Coker headed a Scunthorpe cross back into the danger zone, allowing Iwelumo to nod home from two yards.
The victory is Scunthorpe's first in six matches and helps them climb into the playoff positions.