Schofield curled a fine effort into the net on 65 minutes to cancel out Joe Burnell's first-half opener for a Northampton side looking for their fifth away win of the season.
The home side created 18 clear-cut chances and it looked as if it was not going to be their day until Schofield latched on to Gary Taylor-Fletcher's pass and curled a shot into the top right corner from about 12 yards.
Andy Booth rattled the bar with a header on 40 minutes and the effort was sandwiched between two goalbound strikes that Northampton cleared off the line.
First Burnell reached Booth's header just in time and then Cobblers skipper Scott McGleish prevented Michael Collins scoring with a lob after keeper Mark Bunn punched a cross straight to him on the edge of the box.
Northampton played well in the opening period using a fluid 4-5-1 system that saw wide men Pedj Bojic and Ryan Gilligan supporting lone front man McGleish.
The system produced the opening goal when Gilligan forced Town defender David Mirfin into a mistake and the winger seized possession before squaring for Burnell to score with a close-range tap-in.
Bojic tested Huddersfield keeper Matt Glennon from distance early on and McGleish headed wide from David Hunt's long throw just before Burnell gave Northampton a deserved lead.
But the home side, now without a win in seven games, controlled the second half and had already fluffed four great chances when Schofield finally equalised.
Matt Young's drilled shot was well saved by Bunn on 48 minutes and efforts followed in quick succession from John McCombe, Andy Holdsworth and Gary Taylor-Fletcher.
The most glaring miss was defender McCombe's header when unmarked ten yards out. He directed a weak effort straight at Bunn from Schofield's teasing cross on 51 minutes.
Once Town were finally level through Schofield they poured forward looking for a winner with Taylor-Fletcher and substitute Luke Beckett going close with headers.
But Northampton, who had lost only once away all season, nearly snatched the points late on but McGleish headed straight at Glennon.
After the game, a small band of frustrated Huddersfield supporters called on Town chairman Ken Davy to quit - the third such protest so far this season.