Cutting in from the right, the forward rifled an unstoppable left foot shot from 25 yards into the far corner of the net, leaving the Rochdale
goalkeeper Peter Kurucz with no chance.
It was a deserved victory for Scunthorpe who were always the more positive side.
But with three new faces in their line-up, they took time to settle in a first half devoid of much goalmouth action.
One of those new faces, loan signing Jon Parkin from Cardiff, who made his physical presence felt up front and he came close to a debut goal early in the second half with a shot which brought the best out of Kurucz.
Rochdale, without a goal in their previous five away games, struggled up front again.
They might well have been in front on the hour with their one chance of the match when Nicky Adams could only stab the rebound wide of a gaping goal after skipper Gary Jones had produced a surging run into the box to get in a shot which was well blocked at full stretch by keeper Sam Slocombe.
Four minutes later the Iron broke the deadlock with Thompson's fourth goal of the season to leave Rochdale tasting defeat for the first time since the arrival of new manager John Coleman.