The Cuckoos skipper equalised on 70 minutes to make it 2-2 and then smashed an 81st minute penalty past Sam Arnold to take the points.
Sporting had travelled to their Cambridgeshire hosts looking for a fourth straight win but fell behind to a 10th minute strike from Pierre Omombe-Epoyo.
But the visitors were level by the break when Tamworth loan signing Cameron Howkins converted.
The visitors began the second half strongly and were soon in front when James McGrady struck in the 49th minute.
But with a fourth win in sight for Ian Rowe's side, Cotton pounced to give lowly Yaxley their third victory on the bounce.