A hat-trick from Nathaniel Mendez-Laing did the damage while Nicky Ajose’s late penalty gave the Town some hope late on.
Martin Ling’s first Town side included two changes to the team that had lost at Wigan the week before. In came Jonathan Obika and Louis Thompson for James Brophy, who dropped to the bench and Ben Gladwin, who was not given permission to play by his parent club, Queen’s Park Rangers.
Swindon started patiently, holding onto the ball for the majority of the opening period before the first chance fell to Louis Thompson, who drilled a shot over the crossbar.
At the other end, Callum Camps flicked Peter Vincenti’s knock-down wide before Jon Obika rounded Josh Lillis in the Dale goal and put the ball in the back of the net only to have his effort ruled out for offside.
Moments later, the hosts took the lead. A corner was only half-cleared by Town and Nathaniel Mendez-Laing was on hand to prod home the loose ball from close range.
Lawrence Vigouroux then twice kept out Joe Bunney; first from a header then from a low, driven effort while Louis Thompson went close for the Town, barrelling his way through a challenge before sending a shot just wide of the target.
Swindon’s task was made even harder at the start of the second period. Seconds after the re-start, Mendez-Laing doubled his and the Dale’s lead, slamming home from 12 yards after a deflected cross from the right landed kindly for him in the box.
After Jon Obika’s acrobatic overhead kick landed wide of goal, the home side were awarded a penalty when Brad Barry hauled down Joe Bunney in the box. Mendez-Laing stepped up and drilled his shot down the middle to claim his hat-trick.
However, straight from the kick-off, Barry was hacked down on the edge of the Dale box and Town were awarded a penalty of their own. Nicky Ajose took charge of the situation, tucking his spot kick into the corner to reduce the arrears.
Obika saw a shot deflected wide before he was withdrawn and substitute, Fabien Robert found the back of the net after a well-worked Town move had picked him out in the middle but, like with Obika’s effort in the first half, the offside flag denied the visitors another goal and the hosts held on to book their place in the next round of the FA Cup.