Goals from Jordi Hiwula, Devante Cole, Adam Drury and an own goal from Aaron Oakley meant the Blues progress through to the fifth round and a home tie against Fulham.
The game started fairly even, with both sides enjoying fleeting spells of possession, but the match exploded into life when the City took the lead on seven minutes through leading goal-scorer Hiwula, who calmly finished past Leigh Bedwell.
The goal gave City the initiative and the drive to press forward, with former Robins’ winger Alex Henshall causing numerous problems for the hosts with his pace and trickery at a ground he is more than familiar with.
City deservedly doubled their lead after 25 minutes when Hiwula turned creator after the striker’s darting run through midfield set up Cole who made no mistake from close range.
Two goals to the good, Adam Sadler’s side then virtually ensured their passage to the next round with a third goal before the half-hour mark.
Created by Albert Rusnak and delivered across by Henshall, skipper Drury arrived right on cue to make it 3-0 and leave the impressive 1,601 home crowd crestfallen.
...Swindon U18s 1 City U18s 4
At least the Swindon fans had something to cheer before the break with Robins’ full-back Luke Murden grabbing a goal back with a stunning 40-yard strike and it was almost 3-2 when defender Chris Sim hit the bar in the final seconds of the half.
The second half didn’t continue at quite the same tempo, but the Blues made sure of the result through an unlikely source, with Drury’s cross into the box bundled past his own keeper by Swindon defender Oakley.
The hosts pressed forward in search of a lifeline with Miles Storey coming closest to finding the net, but City defended well and stood firm to make sure of progression into round 5.
Head of Academy Mark Allen was understandably thrilled by the team’s performance.
“I’m delighted with the victory,” he beamed. “Any win in the FA Youth Cup is a good one. We knew it was going to be tough and all credit to Swindon because they gave everything and tried to play football. I just think on the night we delivered everything we hoped we could.
“The lads were definitely up for the game; they were superb from start to finish and deserved the result. The movement and rotation of the players for the third goal was fantastic. It was a great team goal. We showed great penetration and great finishing.
“The cup’s the cup. We’ve got Fulham in the next round, it’s a home tie and we’ll have a go. If the lads match their endeavour for the next game then we’ve got to believe that we have got a chance.
“I know it’s an old cliché but we just take one game at a time and we’ll prepare properly. But right now our focus shifts immediately to our next League match and that’s Liverpool on Saturday.”