Dele Alli’s second half strike proved enough to separate the Reds from Premier League runners-up Tottenham Hotspur at Wembley Stadium.
Alli’s close-range goal sends Spurs into round four despite a thoroughly encouraging and gritty Reds display.
Spurs made a direct start, new signing Juan Foyth heading Kieran Trippier’s corner delivery inches wide of Adam Davies’ post.
Although primarily still on the defensive, the Reds grew further into the game and had bursts forward through Ryan Hedges and Ike Ugbo. Spurs continued to play the ball around quickly, pressurising a Reds defence which looked alert in the first quarter of the match.
The hosts nearly made their pressure tell when they were gifted another header from a set-piece delivery, this time Fernando Llorente nodding just over the top with a golden chance to open the scoring.
The first period was by no means a cagy affair, with Tottenham regularly foraging into the Barnsley area. Hecky’s visitors had a great opportunity to take a surprise lead themselves through Harvey Barnes, who looked to be clean through but for a timely last-ditch Foyth challenge.
With five minutes remaining of the half, Hedges’ corner found Liam Lindsay who headed just wide. Tottenham appeared to bide their time as the Reds carried on their organised defending, restricting their opponents to poorly hit shots from distance as the first half drew to a close.
Half Time: Tottenham 0-0 Barnsley
Things looked promising going into the second half, and the Reds could have hit the opener just 15 seconds into the half as Ugbo found acres of space with a bouncing ball, firing a powerful effort at Michel Vorm from 10 yards before some fans were barely back in their seats.
Spurs continued to utilise their class and threatened through Alli, the England midfielder rolling a shot from distance narrowly past the post.
In a hugely entertaining spell of play on the hour mark, with both sides committing men into attack, Davies superbly denied Harry Winks with a near-post save as Spurs grew increasingly frustrated.
And when a cross from Ryan Hedges struck the arm of Trippier as the Reds continued to give as good as they were getting, the appeals were turned down by referee Tim Robinson to give respite to the Premier League outfit. The encounter was opening up more and more.
As the scoreline threatened to tilt at any moment, it was Tottenham who broke the deadlock with 25 minutes left to play. The home side’s pressure down the flanks proved too much this time as Trippier surged to the byline and cut back for Alli, who was on hand to stroke home a simple finish.
Adam Hammill and George Moncur were introduced as Hecky tried to throw on his exciting trump card players, as Spurs sub Georges-Kevin N’Koudou was denied on his left foot by a strong Davies stop. A final change saw Tom Bradshaw replace Joe Williams as the Reds looked to gamble on their slender deficit; Eric Dier was brought on for Tottenham to preserve the advantage.
In an attempt to seal their passage to round four, both Son and Alli denied well by Davies, who had been at times late on keeping Barnsley in the tie.
Goalscorer Alli was replaced late on for 17-year-old Tashan Oakley-Boothe as the Reds tried in vain to build a final attack.
Spurs wound the clock down and consequently put an end to an intriguing cup campaign early this season for Hecky’s Reds, who put in a dedicated shift and could easily have gone into the hat themselves on another night, backed all the way by a loud and proud pocket of travelling support.
Full Time: Tottenham 1-0 Barnsley
Tottenham: Vorm, Trippier, Vertonghen, Son, Sissoko, Llorente (N’Koudou 67), Dembele (Dier 79), Alli (Oakley-Boothe 90), Foyth, Winks, Walker-Peters.
Subs not used: Gazzaniga, Alderweireld, Kane, Eriksen.
Reds: Davies, McCarthy, Fryers, Williams (Bradshaw 79), Macdonald, Lindsay, Barnes (Hammill 71), Ugbo, Potts (Moncur 71), Hedges, Bird.
Subs not used: Townsend, Jackson, Pearson, Thiam.