Diamonds looked to be heading for victory in the Evo-Stik League South Division One Central after Declan Rogers had put them in front with a fine long-range strike.
But Rory McAuley was the late hero for the Linnets as he grabbed the equaliser in the final play of the game.
There were chances for both teams in an open first half with Ben Heath saving a Harry Limb header while Jack Bowen was denied by the post after he rolled the ball past the goalkeeper having been sent through on goal.
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Heath produced another excellent save from Limb early in the second half and Diamonds took advantage when they broke the deadlock on 56 minutes.
Rogers found space and then launched a superb left-footed strike into the far corner.
The hosts hit back and Heath had to be at his best to turn a Michael Gash header around the post before he also parried away a Ryan Hawkins effort.
Diamonds had the chance to wrap it up late on when Bowen couldn’t quite connect with Nathan Hicks’ low effort across goal.
And they paid a heavy price in the fifth minute of stoppage time when McAuley headed home a free-kick from close-range.
Diamonds are back in action on Tuesday night when they take on Coalville Town at Hayden Road.
Corby Town fought back from 3-1 down to keep their unbeaten record in the Evo-Stik League South Division One Central intact as they drew 3-3 at Dunstable Town.
The two teams drew by the same scoreline in the Emirates FA Cup earlier this season and it was Corby who drew first blood on this occasion with Elliot Sandy converting Jordon Crawford’s cross on 22 minutes.
The lead didn’t last long though as Arel Amu equalised and then the same player put Dunstable in front after the break.
The Steelmen looked to be heading for defeat when Chris Wreh made it 3-1 but Crawford scored from a cross from substitute Sam Grouse to give them hope.
And they earned themselves a point with 12 minutes to go when Greg Ling fired home after Sandy had laid the ball off to him.
The Steelmen now have a big top-of-the-table clash to look forward to on Wednesday night when they take on Bromsgrove Sporting, who lost their unbeaten league record in a 5-1 defeat at Bedford Town this weekend, at Steel Park.