Rangers had been firing blanks up to Chery’s 84th-minute winner and even £15 million-rated Charlie Austin struggled for chances.
Chery, signed from Groningen in the summer on a three-year deal, scored his third goal of the season to show that Austin and winger Matt Phillips may not be badly missed if they leave in the transfer window.
Rangers have turned down a £12 million bid from Leicester for Austin but QPR’s 18-goal top scorer from last season could still leave the club.
And Phillips, also of interest to West Brom and Crystal Palace, may join him out of the Loftus Road exit.
But it was Chery who looked the biggest threat throughout the game and he got the goal he deserved to claim all three points late on.
After a fast-paced attack, Massimo Luongo crossed into the box, Phillips missed it but Chery, at the back post, made no mistake to fire under the keeper.
Austin could have scored in the first half but was inches away from sliding home Chery’s cross into the box after Town defender Tommy Smith had given away the ball in midfield.
Chery also deflected over an Austin shot and only another likely departure – midfielder Jacob Butterfield – could muster much for the home side. Butterfield has been subject of repeated bids from Derby.
Huddersfield had chances in the second half but dangerman Sean Scannell ran out of steam and was substituted while Ishmael Miller’s giant presence caused problems but keeper Rob Green punched away his looping header.
Phillips brought a brilliant save from Town keeper Joe Murphy in the 67th minute as Rangers started to hit their stride.
They finished the game strongly and when Chery broke the deadlock at the death there was no way back for Huddersfield, who are still without a win this season.