Substitute Danny Cadamarteri raced to the byline in the second of five minutes of added time for Cheltenham's time-wasting and crossed for Anthony Pilkington to nod on and Butler to score.
The visitors looked set to register only their second away win this season when they raced into a two-goal lead in a pulsating contest.
Former Leeds striker Leon Constantine scored on his debut after joining on loan from Northampton when he punished a mistake by Huddersfield's Tom Clarke by firing into the roof of the net inside five minutes.
The contest turned nasty in the second half when Cheltenham's Josh Low was sent off for stamping on Clarke in the 61st minute.
The visitors were 2-1 up by that stage. Elvis Hammond raced onto Andy Gallinagh's long ball and cut inside Butler before netting with a neat close-range finish after 18 minutes.
Huddersfield's Michael Collins hit the crossbar from distance before Cadamarteri pulled a goal back from a Gary Roberts' cross before the break.
The home side dominated after Low's dismissal but it looked as if they had blown their chance to earn a point when Robbie Williams missed a penalty in the 84th minute, awarded for a trip on Michael Flynn.