Cotterill, who quit the Potteries two years ago after only 13 games, received a predictably rough ride.
But he was cheered when Cahill, on loan from Aston Villa, bundled home the winner 12 minutes from time to give the visitors a deserved victory.
Stoke goalkeeper Steve Simonsen saved brilliantly from Ian Moore, while Tony Pulis' side struggled to create any clear scoring opportunities.
Burnley manager Steve Cotterill: "It was a hot reception and fully expected and I don't blame the Stoke fans but I'll keep silent.
"I was delighted with the display of my players and this was a great result. We've had a good day and that's it.
"I don't want to open up old wounds. I feel sorry for Stoke as they've played a lot more than us over Christmas."
Stoke: Simonsen, Buxton, Thomas, Duberry, Hall, Russell, Eustace (Greenacre 71), Henry, Clarke (Neal 78), Akinbiyi, Noel-Williams.
Subs Not Used: de Goey, Palmer, Denny.
Burnley: Jensen, Camara, Cahill, McGreal, Duff (Roche 43), Sinclair, Branch, O'Connor (Chaplow 85), Hyde, Moore, Grant.
Subs Not Used: O'Neill, Pilkington, Sanokho.
Goals: Cahill 79.
Ref: P Joslin (Nottinghamshire).