Schofield hit a rising drive into the top right corner of the net after substitute Mark Hudson's low cross was not cleared by the Tranmere defence to score his fifth goal of the campaign.
It is the third time that Huddersfield have scored late on at home to snatch unlikely victories following last-gasp efforts against Bristol City and Brentford.
Town have also scored in all 13 league and cup matches this season with leading Pawel Abbott topping the charts with nine goals so far.
But the former Poland under-21 international missed a hotly-disputed first-half penalty as a drab contest looked to be heading for a 0-0 draw.
Abbott's tame spot-kick was easily saved by John Achterberg on 30 minutes after Tranmere defender Ian Goodison was adjudged to have handled in the box.
The decision was harsh as the ball clearly hit Goodison on the chest and the video replays proved the injustice but the miss made amends for the bad decision.
Tranmere had the game's best chance in the first half but Delroy Facey dragged a shot wide of the target from close range after being put through by Chris Greenacre.
Recent signing Nicky Summerbee forced Town keeper Paul Rachubka into a fine save from a 25-yard free-kick on 48 minutes.
That was as good as it got for either side in a game that featured plenty of passing football but little goalmouth action until the closing stages.
Huddersfield boss Peter Jackson brought on substitutes Gary Taylor-Fletcher, Hudson and Junior Mendes late on to pep up the attack and it worked as Town created a flurry of late chances.
Schofield finally broke the deadlock after missing an earlier effort created by Andy Booth's knockdown.