Blues got off to the worst possible start after 2 minutes when slack defending allowed Paul Mullin to cross for Matt Crooks in space, who side-footed it home.
The Terriers, who have already been crowned Professional Development League 2 champions, continued to trouble the away side and soon got a quick second.
Mullin picked up the ball 25 yards from goal and curled the ball beautifully into the top corner, with Connal Trueman at full-stretch unable to get close.
Despite Huddersfield's two-goal advantage, Birmingham refused to cave in and continued to be confident in possession and plough forward.
A lofted ball from the defence fell kindly for Asante after the home side failed to clear it, and he capitalised in style calmly placing the ball past former Blues 'keeper Ian Bennett.
Liam Truslove fired a shot from long-range that tested the palms of Bennett. Chances from Matt Crooks and Jake Carroll kept Trueman on his toes, but he averted the danger with fine saves.
A swift counter-attack brought Blues back on level terms. Scott Allan raced free and shrewd movement from Asante enabled the through ball to find his path, and he calmly slotted beyond Bennett.
The second-half began with both teams looking sprightly and assured, but lacking the cutting edge in the final third.
Asante collected the ball inside the box, turned and fired into the top corner to complete his hat-trick and put his side ahead for the first time in the match. The Dutchman continued his one-man crusade and quickly got a fourth to put a bit of breathing space between the two teams.
Allan took advantage of careless defending from Carroll to break free and play it to Asante, who with poise sent the keeper the wrong way, easing it into the bottom corner.
The hosts then surged forward in a bid to rescue their 100% home record, with Crooks and substitute Jake Charles having efforts well saved by Trueman.
Blues weathered the storm and have now won seven out of their last eight games, subjecting their opponents to only their third loss of the season.
Blues U21s: Trueman, Dacres-Cogley, Bernard, Cooper, Fry, Webb, Allan (O'Neill 79'), Truslove, Asante (McGee 72'), Arthur, Hales (Dunbar 82').