After a tight first half with few chances, Ian Watson’s men worked themselves into the ascendancy after the break, with Hayes’ late goal proving just rewards.
There were three changes to last weekend’s starting line-up that beat Fleetwood Town 2-1. Nils Ramming returned in goal, as did Ed Francis and Sam Sherring, with Tobi Adebayo-Rowling suspended. Sam Beckwith returned to the squad after a period away with injury.
Dale were the more dominant of the two teams in a first half that saw few chances created by either side.
Aden Flint headed an early chance narrowly over the bar, before Watson was forced into an early change as Luke Hannant replaced the injured Jonny Smith.
Swindon also created an early chance, but Anthony Munda’s shot was superbly blocked by Aden Flint.
They created a couple of chances after the break, with Ramming making a fine save down low to deny Antwoine Hackford’s effort from inside the area. Aaron Drinan also shot wide for the visitors.
From there though, Dale began to turn the screw. Glenn Middleton beat his man out wide and crossed low into the box for Dajaune Brown, who miscued his effort from a yard out.
Substitute Hayes caused problems for the Swindon defence after his arrival, and when he was brought down by Kaelan Majekodunmi in the 85th minute, the visitors were reduced to ten men.
From the resulting free-kick, Man of the Match Charlie Tasker was denied by a stunning save from Connor Ripley, with a number of Dale efforts blocked on the follow-up.
However, there was nothing they could do to deny the late winner. Middleton’s cross fell for Flint, whose shot skewed towards Hayes. He adjusted superbly to flick the ball into the top corner with his head.
Despite seven minutes of added time, Dale held out superbly, picking up a third win in a row.
Dale XI | Ramming, Tasker, Wilson, Gilmour ©, Francis (72’ Dieseruvwe), Adeeko, Smith (23’ Hannant (72’ Hayes)), Sherring, Brown, Flint, Middleton.
Unused subs | Waller, Silcott-Duberry, Beckwith, Henderson.
Scorers | 88’ Hayes.
Swindon Town XI | Ripley, Negru, Ball, Nichols (69’ Clarke), Majekodunmi, Drinan © (83’ Hungbo), Thomson (90+2’ Millard), Butler, Munda, Hackford, Kirkman (90+’2 Butterworth).
Unused subs | Ward, Debayo, Pearman.
Attendance | 4,235 (530 away).
Report by Jack Booth.