The hosts scored in the 20th minute and had by far the better chances before Barnsley had a goal ruled out in injury-time for the second game in arow.
The Reds have not won in their last 18 away games in all competitions since a 1-0 victory at Huddersfield last April.
They offered very little in attack, especially in the first half and, while they improved slightly after the break, they did not have a shot on target.
Poya Asbaghi made six changes from the side that lost 1-0 at home to Cardiff City in the league on Wednesday.
There were full debuts for new signing Amine Bassi and 18-year-old Aiden Marsh from Monk Bretton who has come through the academy.
Jack Walton, Aapo Halme – playing for the first time since September after injury – Romal Palmer and Aaron Leya Iseka also came back into the 11.
Dropping out were Brad Collins, Josh Benson, Remy Vita, Michal Helik, Devante Cole, who were all on the bench, and the cup-tied Domingos Quina.
Barnsley played a 4-4-1-1 with Marsh and Callum Styles on the wings while Bassi was just behind striker Iseka.
After a very quiet start to the game, Huddersfield's Jordan Rhodes had the first chance on 15 minutes as he slid in at the front post to meet Sorba Thomas' right-wing cross but found the side netting six yards out.
The opener arrived five minutes later as Thomas' long ball from the right totally split centre-backs Mads Andersen and Halme so Josh Koroma was free to head the ball into the path of Duane Holmes who ran into the box and beat Walton one-on-one. It was an extremely soft goal, as Halme had been sucked into midfield and Andersen was left marking two players.
Barnsley almost levelled within a minute in bizarre circumstances as Kitching's left-wing cross was touched beyond the home goalkeeper by Town defender Naby Sarr but it hit the inside of the right post and stayed out.
Koroma could have doubled the lead after being played in on the left of the box by Jon Russell, following an excellent run, but his shot was kept out by Walton diving to his left. Russell then sent a looping header from 15 yards onto the roof of the net.
Former Barnsley defender Matty Pearson then headed well wide from a right-wing corner under pressure from Halme.
Jordan Williams gifted his former club a huge chance on the stroke of half-time as he chested the ball into the path of Koroma who was clean through on goal but Walton blocked at his feet then Andersen put in a good tackle from the rebound.
Huddersfield had been easily the better side in the first half, and should have been further ahead, with Barnsley offering very little in attack.
Asbaghi made three changes at half-time with Halme, Marsh and Iseka replaced by Helik, Benson and Carlton Morris.
Barnsley were better at the start of the second half, but struggled to create clear opportunities with Kitching heading over a difficult chance from a Benson cross on 62 minutes. Minutes later, Morris cut in from the left wing and curled wide of the top right corner from about 15 yards.
Huddersfield then had a good spell with substitute Ollie Turton netting from close range but the flag rightly went up for offside as he latched onto Danel Sinani's header. Sinani then shot wide from 20 yards after good work from Rhodes.
The hosts then saw substitute Danny Ward smash a ten-yard volley off the left post after a left-wing cross by Josh Ruffels.
Thomas should have netted minutes later when another left-wing cross was headed down by Sinani and Thomas blasted straight at Walton eight yards out then fired the rebound over.
Helik thought he had levelled in injury-time when he headed in but the goal was disallowed for a push by Bassi on Pearson.
Russell should have made it 2-0 in injury-time when he was put clean through but he shot wide.
Huddersfield (4-3-3): Blackman; Pipa (Turton 31mins), Pearson, Sarr, Ruffels; Holmes, Russell, Eiting (O'Brien 60); Koroma (Sinani 60), Rhodes, Thomas.
Unused: Nicholls, Toffolo, High, Ward, Lees.
Yellow cards: Koroma.
Goals: Holmes 20.
Barnsley (4-4-1-1): Walton; Williams, Halme (Helik HT), Kitching, Andersen; Marsh (Benson HT), Gomes, Palmer (Cole 78mins), Styles; Bassi; Iseka (Morris HT).
Unused: Jinadu, Collins, Hondermarck, Vita, Thompson.
Yellow cards: Kitching, Helik.
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