Florian Tsaguim gave the visitors an early lead in the 6th minute and as half-time approached Adam Murray doubled their advantage. Ed Cook gave The Blues a lifeline shortly after the restart but Juwon Akintunde scored Royston's third to seal a fourth consecutive defeat for United.
Brad Munn and Lewis McGugan made three changes to the side that played midweek - Basford United Loanee Zayn Hakeem made his debut up front, while Ed Cook returned at centre-half and Curtis Davies earned a first start of the season.
The visitors started with a high press that very quickly paid dividends. A weak pass back to Ross Durrant landed the goalkeeper in trouble as his attempted clearance was blocked by Tsaguim and tapped into an empty net to put the visitors ahead after six minutes played.
Royston almost made it two on the half-hour mark, the ball pinballed around the box and found the feet of Gregory Sandiford who was denied by the woodwork, the rebound fell to Tsaguim but Durrant was equal to the striker’s effort.
Two minutes later the visitors' captain Murray doubled their advantage as he rose highest and found the back of the net with a looping header.
Then Joshua Coldicott-Steven’s had a great chance to net the third, the midfielder chested down a lobbed pass from Tsaguim but could not hit the target with his volley.
In first-half stoppage-time Marley Fearon won a free kick in a dangerous position which Cieron Keane stepped up to take. Keane beat the wall with his set piece but it was caught comfortably by Louis Chadwick in the Royston goal.
With the last action of the half Micah Jebbison found space to run and deliver a cross from the right flank but Chadwick was quick off his line and claimed the ball before it could reach Kam Campbell or Hakeem.
Long Eaton United picked up from where they left off at the break and reduced the deficit just two minutes after the restart. Cook scored with a thumping header at the back post after a great corner from Callum Cocks.
However, the visitors restored their two-goal cushion in the 66th minute, half-time substitute Akintunde slid and knocked the ball across the line after a perfectly weighted through ball from Tsaguim.
Moments later Tsaguim had another chance of his own but Durrant made a superb save from close-range to deny the striker his brace.
Chances came few and far between as the second half progressed and, despite some positive substitutions, Long Eaton could not find a way back into the match.