Thompson appeared to have been flagged offside as he gave the Iron an early lead, but the goal stood to the fury of Reading boss Brian McDermott.
Gylfi Sigurdsson drew the Royals level with a typically fine hit but giant centre-half Rob Jones was able to head in a second-half winner for the visitors.
Nigel Adkins lost top scorer Gary Hooper to Celtic in pre-season and former Rochdale man Chris Dagnall had the task of filling his boots at the Madejski Stadium.
Dagnall was quiet throughout in a professional performancfrom Scunthorpe who are expected to struggle this season.
Reading were superb after Christmas last season and could impress again after playing well enough in a narrow defeat.
Jimmy Kebe had the first effort with a powerful strike from 20 yards but goalkeeper Joe Murphy was able to let it comfortably clear the crossbar, before Kebe again threatened with a header which drifted wide.
But it was the visitors who opened the scoring in the ninth minute from their first attack in contentious circumstances.
A ball over the top was collected wide on the left by Jonathan Forte and, despite the linesman raising his flag, he crossed for Thompson to convert from close range.
The Royals backline had all but stopped upon seeing the flag, and were left incensed when referee Fred Graham overruled his assistant to award the goal.
McDermott's side responded well however, and were level in the 26th minute through Sigurdsson.
The Icelandic midfielder was one of the players to watch in the Championship last season as he scored 20 goals, and he showed his prowess again with another fine finish.
Sigurdsson beat two men 25 yards from goal before smashing a strike beyond Murphy and into the top corner.
Jobi McAnuff then dragged an effort across the face of the goal as Reading surged forward but the sides went in to the break on level terms.
The visitors were keen to see half-time but started the second period well and went ahead through Jones on the hour mark.
Michael O'Connor swung over a corner and 6ft 7in Jones towered over everyone to thump a header past Adam Federici and into the roof of the net.
Sigurdsson sent a free-kick narrowly over and substitute Simon Church had an effort saved as the Iron held on for all three points.