Taylor-Fletcher headed over from close range before Danny Schofield struck the post with a shot as Huddersfield wasted some gilt-edged chances.
Martin Devaney skimmed the crossbar with a shot for Barnsley but they struggled to create clearcut chances.
And Taylor-Fletcher put the visitors ahead when he bundled in after a mix-up in the Barnsley defence.
Barnsley boss Andy Ritchie:
"It is half-time. We have a good chance to go there and turn the tie around. "We are quite capable of doing it. They probably edged it; they mixed their game up a bit better than we did - but we are still in the tie.
"The players are not down; it is only half-time, and we know we can play better - 20 or 30% better."
Huddersfield manager Peter Jackson:
"We have got a tough 90 minutes back at the Galpharm Stadium.
"Barnsley are a quality side, and we won't be taking anything for granted.
"The most important thing was to keep the tie alive - and we have certainly done that."
Barnsley: Colgan, Hassell, Reid, Kay, Heckingbottom, Shuker, McPhail, Howard, Devaney, Nardiello (Hayes 71), Richards (Wright 71).
Subs Not Used: Flinders, Tonge, Williams. Huddersfield: Rachubka, Holdsworth, Nathan Clarke, McIntosh, Adams, Taylor-Fletcher, Worthington, Hudson, Schofield, Graham (Abbott 75), Booth.
Subs Not Used: Senior, Brandon, Mirfin, Ahmed.
Booked: McIntosh.
Goals: Taylor-Fletcher 85.
Att: 16,127
Ref: P Taylor (Hertfordshire).
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