Stevenage went into the match on the back of six straight Sky Bet League One defeats and it was left to Dunne to breathe life into the visitors' season in the second minute of time added on.
County's Callum McGregor and Shroot both shot over the crossbar in the closing stages of the first half before Stevenage grew in confidence after the break.
But it took until injury time when Shroot's endeavour down the left gave Dunne the simplest of finishes and left Magpies boss Chris Kiwomya ruing a number of injuries.
"We didn't deserve to get beaten," he said. "We got a number of good balls into their box and created opportunities, but nothing fell for us in their box.
"We were without a number of players and brought in Adam Coombes up front when Danny Haynes reported a knock.
"They're a difficult team to play against. They're big and physically strong and we've matched them, even at set pieces, which is their strength
"There are a lot of positives to take from our display. We are not far away, but we've got to make the right decisions in the right areas.
"I'm pleased with the players and the work-rate and we will be ready for Liverpool on Tuesday.
"We want to go out there and give a good performance and enjoy it as much as we can. It's a bonus for the club."