Barnard, on loan from Spurs, beat calls for offside to slot home the opener in the 19th minute and Crewe set about defending the lead.
On the back of five defeats in six matches, Crewe worked really hard, but skipper Booth plundered a point five minutes from time.
Barnard, who scored on his debut against Town in his first loan spell in September, tormented the home side again.
Mark Carrington's through ball left the Huddersfield players screaming for offside but Barnard, in splendid isolation, ignored the jeers and beat Matt Glennon.
Crewe played some neat football and grew in confidence, while Huddersfield, with seven wins in the last 10 games, were out of sorts.
Only Booth and striker partner Phil Jevons emerged with credit.
Huddersfield were dominant for long periods after the break but could not prise open the Crewe rearguard.
Marshalled by Julien Baudet, the Railwaymen denied Town time after time while barely escaping their own half.
Booth almost levelled in the 63rd minute when Robbie Williams dummied and sent over a superb cross which saw the veteran striker force a fine stop from Ben Williams.
Jevons turned creator for the Town leveller when he took the near-post corner which allowed Booth to head low beyond Williams.
Town kept going and midfielder Michael Collins almost stole the points in the 90th minute but dragged his shot across the face of goal.