Rangers hot-shot Paul Furlong scored twice as the visitors moved a step closer to the play offs.
Veteran Furlong, 35, has now scored five goals in five matches and showed none of the Premiership class he gained during a lengthy spell with London neighbours Chelsea.
Furlong out-muscled Town defender Nat Brown on five minutes to latch onto a Kevin Gallen throughball to put Rangers ahead.
And he secured the win in the third minute of stoppage time by coolly stroking home a close-range shot from substitute Tommy Williams' cross.
In between, defender Danny Shittu scored when he was the first to react to Gallen's close-range header when it re-bounded off the right-hand post on 39 minutes.
The visitors dominated most of the match and always looked a yard sharper than relegation haunted Huddersfield.
But the match could have been different had Town winger Simon Baldry done better when twice in the clear against the run of play.
Baldry was put through on 14 minutes by Martin Smith but a terrible touch allowed Rangers' keeper Chris Day - making his first start after a 16-month lay off recovering from a double leg break - to comfortably smother the ball.
And on 27 minutes Smith was again the supplier for Baldry to run through on goal but instead of shooting he dragged the ball back and the momentary lapse allowed Shittu to whip the ball off his toes.
Rangers boss Ian Holloway was delighted with his side's performance and said his players reacted in the right way following Saturday's dismal 3-1 defeat at Swindon.
"We were all at sixes and sevens against Swindon and probably should have lost by more," he said. "We had words in the dressing room afterwards and the players have come out tonight and produced a battling display.
"I would have preferred to have got the third goal earlier because Huddersfield have some dangerous players who might have turned the game around but generally I thought it was a very professional performance." And his opposite number Mick Wadsworth conceded his players were second best on the night.
"We tried, worked hard and created chances but we were second best overall," he said.
"But I cannot criticise the players because they have done everything that I asked of them and if we perhaps average one-and-a-half points per game over the closing stages of the season we might stand a chance of staying up."