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The hosts had goalkeeper Alex Smithies to thank for preserving their lead in the 10th minute when he produced an impressive save to deny Henri Lansbury, and it was not long before the Terriers gave themselves some breathing space.
Forest's best chance of the first half fell to debutante Tom Ince just after the half-hour mark, but Smithies proved too good for the Hull City loanee at close range.
Huddersfield were out of sight in the 54th minute courtesy of a peach of a goal from Holt, who thumped home a left-footed drive after good work by Sean Scannell.
Smithies produced another fine save to keep out Britt Assombalonga in a one-on-one situation on the hour mark, while Karl Darlow had to produce an equally-impressive stop at the other end to deny Huddersfield a fourth through Conor Coady.
Forest were second best in every area of the park, but they were unlucky to come away without a goal to their name, as Chris Burke struck the underside of the bar with a late effort that should have ended up in the net.
The result stretches Huddersfield's unbeaten run to seven games and moves them up to 13th in the table.