Rovers shot-stopper Collister, 18, did well to parry a shot from Jordan Rhodes in the 29th minute after Gary Roberts forced defender Ian Goodison into a mistake in the box.
Tranmere boss Les Parry had kept faith with Collister following his impressive performance in the Carling Cup in midweek, despite having Gunnar Nielson on loan from Manchester City.
Collister repaid his manager's faith with a competent display, and he did well again in stoppage-time to deny Roberts, who struck from 25 yards.
Smithies, meanwhile, was alert early on to beat away Terry Gornell's long-range blast, but he was nearly caught out by Enoch Showunmi when attempting to clear Gary Naysmith's poor backpass.
Town's Scott Arfield produced a rare glimpse of attacking flair with a solo run past three defenders after 31 minutes, but he dragged his shot wide from a tight angle.
An equally sterile second half was only notable for Tranmere's Joss Labadie breaking away down the left. But he snatched at his shot and ballooned the ball over the crossbar from 25 yards.
Huddersfield's miserable afternoon was completed in the 86th minute when Scotland international Naysmith was sent off for a second yellow card. Naysmith brought down substitute Kayleden Brown on the edge of the box.