Stearn pounced after a swerving, dipping free kick from Harvey Bunker had been fumbled by Jonathan North to send the Wiltshire side into delirium.
It capped an eventful final ten minutes, after Eitel Goueth’s 83rd minute penalty had been saved by Chippenham goalkeeper Will Henry.
Joint manager Jon Underwood admitted that the result left him feeling physically sick, and that he felt “the result had 1-0 Slough written all over it”. After missing the chance from 12 yards, he couldn’t have believed that his side would go on to lose it.
Goueth fired an early chance over the bar on the volley with both sides feeling their way into the game.
The Rebels enjoyed their best spell of the first half just past the 20 minute mark. A long pass from Matt Lench was controlled expertly by Freddie Grant, who moved into the penalty area and found Max Worsfold but the winger’s effort was saved.
More super football followed, with Goueth and George Hunt linking up in midfield to release lone striker Tom Derry, but Will Henry saved his low strike.
It took a super save from Jonathan North to keep out Alex Bray’s dipping long range strike on 34 minutes, the keeper getting a strong hand to the ball to turn it over.
Chippenham broke away minutes before the interval, but Harry Warwick’s tame effort was an easy save for North.
Marlon Jackson went close early in the second half as his deflected shot hit the side netting.
Joe Lawal was introduced on 64 minutes and almost had an immediate impact as he went to ground, only to see his penalty appeals waved away.
Minutes later, the Rebels had George Hunt to thank for a fantastic tackle which denied a certain goal.
But with eight minutes remaining, substitute Gabe George’s shot was blocked by an arm, and Dale Wootton pointed to the spot. Up stepped Goueth – who celebrated his 20th birthday yesterday – but Henry plunged low to his right to make a brilliant save.
Two minutes into stoppage time, the visitors almost found a goal but Jackson’s shot rolled across the face of goal.
And Slough were punished for a foul by Ryan Bird, as Stearn reacted quickest to score after the initial shot from the free kick was saved by North.
Image: Philip Benton
Chippenham Town Line up
Will Henry, Alex Bray, Will Richards, Kieran Parselle, Vincent Harper, Adam Mann, Joe Hanks (Dan Griffiths 88), Harry Warwick (Ross Stearn 59), Luke Russe, Alefe D’Abadia (Harvey Bunker 66), Marlon Jackson. Unused substitutes: Spencer Hamilton, Jennison Myrie-Williams.