Alfreton moved out of the Blue Square Bet Premier relegation zone with a win over nine-man Bath.
Adam Connolly headed the visitors in front, before Gethin Jones was sent off for a foul on Anthony Wilson, causing a melee amongst the players.
Sean Canham saw red for violent conduct in the aftermath of this incident, before Nathan Jarman scored a penalty after Glyn Garner fouled Paul Clayton.
Craig Clay's strike from the edge of the box sealed the points for Alfreton.
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Bath City manager Adie Britton told BBC Radio Bristol:
"There were a couple of decisions made by the referee and I think they determined the result of the game.
"If you have two men sent off, quite clearly you are not going to win a game of football, so it's disappointing.
"I need to speak to the referee and ask him for an explanation of what happened.
"There are numerous decisions I'd like to discuss with him - following that we need to decide whether we appeal agasint the sending-offs."