Thompson rifled in a 25-yard shot that went in off the underside of the bar to earn a point that had looked unlikely at the break on Sunday.
Forest produced a fine first-half display and surged into a two-goal lead thanks to Joe Garner's cool finish and a glorious George Boyd goal.
But Scunthorpe rallied after the break and reduced the deficit through Niall Canavan's close-range finish before Thompson levelled.
The point saw Billy Davies' men finish third and set up a meeting with Blackpool in the play-off semi-finals, but Davies will be concerned about his side's worrying away form as they picked up just two points from the final 30 available on the road.
The Iron ended what has been a fantastic season with a point. Their safety was assured two games ago and they can now look forward to back-to-back seasons in the second tier for the first time in 46 years.
Forest already appeared to have one eye on next week's play-offs and made eight changes to their side, with Davies opting to rest several key players.
But the changes did not have a detrimental effect as Forest started brightly and almost took the lead when Lewis McGugan's volley from 10 yards was parried by Josh Lillis.
The miss did not prove costly, though, as the visitors went ahead in the 17th minute thanks to a cool finish from Garner.
The Iron failed to clear a long ball from goalkeeper Paul Smith and Garner collected the ball 20 yards out before advancing into the area and picking his spot, low into the bottom corner for just his second league goal of the campaign.
The game opened up as a result of the early goal and both sides created good opportunities.
Martyn Woolford should have equalised after good work from Sam Togwell on the right, but he blazed over at the far post, while David McGoldrick squandered a chance to double Forest's lead when his finish was wayward after wriggling clear of Canavan.
Forest strengthened their grip on the game four minutes before the break with a goal of the highest quality.
Paul Anderson, Garner and McGoldrick were all involved with a series of short passes working the ball from right to left, with McGoldrick slipping Boyd in to finish with a sweet first-time effort with his left foot.
Forest were rampant and could have gone further ahead when Joel Lynch's cross bounced back off the bar but McGoldrick slammed the rebound wide.
Scunthorpe made a roaring start to the second period and Gary Hooper had already seen an effort cleared off the line by the time they reduced their arrears in the 50th minute.
After Forest failed to clear Grant McCann's corner properly, the ball was played back and Smith's parry fell kindly to Canavan who fired home from six yards.
Half-time could not have come at a worse time for Davies' men as they were unable to recreate the energy and attacking prowess of the first period, with Garner's low effort at the near post the only time Lillis was tested.
Scunthorpe continued to push for a leveller as Hooper, in front of watching Celtic manager Neil Lennon, hit the bar with a looping header and Thompson was denied by a low Smith save.
But Thompson had the final say as he thundered a shot home from distance with just two minutes of normal time remaining.