Gary Johnson's side had won just once in their last nine matches going into the game at Selhurst Park and were thumped 5-2 at home by Doncaster on Saturday - leading to their boss expressing fears of a late dogfight to beat the drop.
But Iwelumo, on loan from Wolves, scored only his second goal of the season and his 73rd-minute strike was a rare moment of quality in a forgettable match.
Three Palace defenders tried to clear Liam Fontaine's long throw, but the ball looped invitingly to the Scottish striker, who swivelled to send a right-foot volley over keeper Julian Speroni.
It consigned Paul Hart to a first defeat since taking charge at the Eagles and the South Londoners struggled to create scoring chances in a subdued performance.
The first 45 minutes were dire, although the home side appealed for a penalty when Johnny Ertl's shot struck the arm of City captain Louis Carey.
The visitors played the better football before the break but noteworthy moments were painfully rare.
The second half was not much of an improvement, but Palace wasted their best chance of the game in the 52nd minute when Darren Ambrose's cross was met by Alan Lee - he could only steer his header across the face of goal and past the far post.
City right-back Bradley Orr posed an attacking threat for the away team and smashed one effort over the top before a stinging 64th-minute effort from the edge of the box was parried by Speroni.
But the breakthrough did come for the travellers when Iwelumo, a former transfer target of Palace under previous boss Neil Warnock, doubled his goal total for the campaign.
Hart's honeymoon period at Palace seems to be over as the fed-up home support booed his decision to replace Nick Carle with Stern John with nine minutes remaining - and there were jeers at the final whistle.