Stoke scored after 60 minutes with Wayne Thomas scoring from a header following a free kick on the edge of the area.
A mistake from Eric Sabin saw Stoke score again a couple of minutes later, but the goal was not given, and Swindon were given a free kick from the Stoke hand ball.
Stoke then made in 2-0 a few minutes later, with Iwelumo meeting a cross to score from close range.
A minute into injury time Andy King bought on Juan Cobian who he had said would never play for Swindon again. Cobian replaced Alan Reeves who was injured.
Swindon stay 14th in the table on 54 points.
They meet QPR who beat them 4-0 earlier in the season on Saturday.