Town led on seven minutes at John Smith's Stadium when Mounie set up Alex Pritchard for his first goal since signing in January.
AFC Bournemouth equalised through Junior Stanislas six minutes later but Mounie sent Town in ahead at half-time, converting Aaron Mooy's cross.
It was 3-1 after the break when Mounie's shot deflected in for a Steve Cook own goal.
Despite Mooy being taken off on a stretcher, Rajiv van La Parra made it 4-1 in stoppage time, from a penalty won by Pritchard.
Town move up to 16th, four points behind 10th-placed AFC Bournemouth, who suffered a first loss since 23 December.
Huddersfield Town: 24 Feb v West Brom (A)
AFC Bournemouth: 24 Feb v Newcastle (H)