The on-loan Tottenham striker clinically finished a one-on-one situation after 16 minutes to put the Railwaymen on their way to victory.
Barnard, who is on-loan at the Cheshire side until January, could have added to his tally had it not been for a couple of excellent saves from visiting keeper Matt Glennon.
But Glennon blotted his copybook six minutes before half-time when he charged out of his box to clear a through ball only to miss it completely and allow Eugen Bopp to roll home Crewe's second.
That was harsh on Huddersfield as they had enjoyed the lion's share of possession but they never truly threatened Ben Williams' goal apart from a David Mirfin header which the Alex keeper tipped over the bar.
Barnard made a decisive break when he latched on to a slide-rule pass from Gary Roberts and held off Shane Killock's challenge before shooting in.
The Londoner then cut in from the right flank to force Glennon into a near post save and the keeper did even better to deny Barnard with his legs as he dived the wrong way.
The second half was a non-event as Crewe closed the game out with some sound defending.
And they could have had a penalty in the final minute when substitute Byron Moore looked like he had been pole-axed by Joe Skarz.