Mickael Antoine-Curier's second-half header against St Mirren gave Hamilton a Scottish Premier League lifeline.
St Mirren were down to 10men when the goal came just 16 minutes from full time after Antoine-Curier got up to connect with a Dougie Imre cross.
He could have had a second minutes later but it was saved by the St Mirren keeper.
The game finished with 10 v 10 as Neil was sent off when he picked up his second booking of the game.
The results gives the Accies a chance of survival with just three games to play.