Evan Garnett gave the Blues an early advantage, however, Tom Jones equalised for the hosts moments later to level the scoreline going into halftime.
But it was Jake Avery that immediately in the second half etched Newcastle in front and aided their progression into the Second Round Qualifying.
Brad Munn opted to name an unchanged starting XI to the one that claimed victory over Hinckley LRFC on Bank Holiday Monday.
Long Eaton piled on the pressure in the opening moments of the match, but it was not until the 11th minute that Joe Slinn was called into action for the hosts.
Callum Cocks connected with Liam Loughlan’s cross and redirected the ball towards goal with a deft flick, although it was a comfortable stop for the Newcastle keeper.
Two chances fell the way of Archie White moments later - the first was a shot from distance that had to be palmed around the post by Slinn, and the second was an attempted chip that was caught by the towering keeper.
The Blues did eventually open the scoring in the 23rd minute through Garnett after Ryan Campbell-Gordon beat his man and put the ball on a plate inside the six-yard box for the striker to tap home with ease.
Cocks then forced Slinn into a diving stop right after the restart, when he whipped a free kick from the edge of the box towards the bottom right corner of the Newcastle goal.
However, just four minutes later and slightly against the run of play, despite the crossbar and Lewis King’s best efforts to deny Jake Twyford and Tommy Van Der Laan, it was Jones that netted his fifth Emirates FA Cup goal of the campaign with a rebound volley into the far corner.
The last chance of the first half fell to Carlos Dos Santos when he picked the ball up around 20 yards out and attempted to curl a strike towards the far post – spinning with his back towards goal – but it did not trouble King.
Forty-five minutes had been played and the referee blew for half-time, however, directly from the restart, Avery flew through the Blues' defence and struck the ball with venom into the top right corner to give Newcastle the advantage.
Loughlan then had a chance to equalise on the hour mark, but his scuffed strike was an easy gather for Slinn.
George Lewis could not believe he had not scored moments later, after the ball flew across the goal line for the Newcastle substitute to fire into the empty net at the far post, although somehow the ball was blazed way over the bar.
Within the next 20 minutes, Newcastle’s defence stood firm and solid to deny United multiple half chances from the edge of their 18-yard box.
Cocks came closest with a thunderous strike from 30 yards out late on, although once again the ball just fizzed past the post of Slinn’s goal.
Despite a chance-filled performance from the Blues, Munn’s side were condemned to defeat as the referee blew the full-time whistle and confirmed our departure from the Emirates FA Cup.