The Magpies were out-played and out-thought by a side in their first season in the Football League, with a Mike Williamson own goal, Michael Bostwick and Peter Winn earning victory for the hosts.
And to complete a miserable night, Alan Pardew's men finished the match with 10 men when substitute Cheik Tiote was sent off for a reckless challenge.
The result was also sweet revenge for Stevenage's fans who had seen their side knocked out of the FA Cup by Newcastle famously as a non-league side 13 years ago.
Alan Shearer scored the goals for Newcastle then. This time there was no-one to provide any inspiration against a Stevenage side who were truly magnificent.
At the end Newcastle, six-time winners but who have not won the cup since 1955, held their heads in shame. And well they might.
Pardew had main strikers Andy Carroll and Shola Ameobi ruled out through injury.
It meant Leon Best, who marked his first Premier League start for the club with a hat-trick against West Ham in a 5-0 victory in midweek, retained his place as Pardew made five changes from a starting line-up which saw Alan Smith and Joey Barton in tandem in midfield.
It was just as well that Pardew and Newcastle afforded Stevenage such respect because right from the kick-off the League Two side's attitude was magnificent.
Manager Graham Westley, whose cup pedigree includes taking Farnborough Town to Highbury for a fourth round tie against Arsenal in 2003, sent them out to have a go and in the first half they more than held their own.
Newcastle's best effort, their only real opportunity, in that 45 minutes was a volley from Barton which brought a smart save from goalkeeper Chris Day.
But while Stevenage gave their illustrious opponents respect they also showed that they had the ammunition to cause damage.
They would have gone ahead after 31 minutes but for the brilliant goalkeeping of Tim Krul who was playing in place of Steve Harper, whose wife is heavily pregnant.
Krul dived full length to his right to tip away a blistering 25-yard shot from Bostwick.
But if honours were even at half-time then the second 45 was all Stevenage. The League Two side did not just cope with Newcastle. They pulverised them.
First they shocked Newcastle with the first goal from the impressive Stacy Long after 49 minutes. The midfielder came inside and unleashed a shot which took a deflection off defender Michael Williamson before it nestled in the Newcastle net.
It was no more than Stevenage deserved although Newcastle replied almost immediately with a chip shot from Kevin Nolan which saw Day back-pedalling to tip the ball over the crossbar.
But Newcastle were in big trouble after 55 minutes when Bostwick extended Stevenage's lead. This time Fabricio Coloccini came sliding in for the tackle but the ball slid clear and Bostwick pounced to send a low shot rifling past Krul and into the net off the foot of the post.
It was no fluke. In fact, at times it looked as if the home side were the Premier League outfit.
It got worse for Newcastle when Tiote lunged two-footed at Jon Ashton in a moment of madness. he might have got the ball but it was reckless and referee Andre Mariner had no option but to show the red card.
Newcastle pushed forward in the final 10 minutes, urged on by Barton in particular and he produced a stunning 35-yard right-foot strike in injury time to give Newcastle hope.
But an equaliser would have been a travesty. And it was only justice when Winn raced clear to score with a fantastic finish to put the League Two club in the fourth round and set up the most frantic celebrations in Stevenage's history.