They were second-best for much of the game and were thankful that Callum Brittain was unable to convert two glorious chances as the Championship side dominated the first half.
But Thomas Tuchel's side, reshuffled with no fewer than 10 changes, were able to find another gear after the break and Abraham's tap-in was enough to secure a tie in the next round at home to Sheffield United.
Story of the match
If Chelsea did not know exactly what to expect from their Championship opponents, they quickly found out. Barnsley pressed high with extreme intensity right from the off, barely letting their prestigious visitors out of their own third, and both Cauley Woodrow and Herbie Kane failed to capitalise on stolen possession before they created a huge chance.
Skipper Alex Mowatt was released down the left by Kane, and he turned inside before playing a cross which took a flick on its way to Brittain at the far post. The wing-back was charging in but had to adjust to poke an effort on goal, and he was unfortunate to aim straight at the legs of goalkeeper Kepa Arrizabalaga when anywhere else would have been a certain goal.
When Barnsley’s intensity did inevitably drop a little, Chelsea showed some promising touches but little sustained threat. They should, however, had had a penalty, when Toby Sibbick slid in on Abraham with what on first viewing looked a perfect challenge, but in fact caught the foot of the striker instead of the ball.
Their only other real opening saw Christian Pulisic fail to turn in a Callum Hudson-Odoi cross on the stretch, and it was Barnsley who went into half-time with more regrets after another big scoring opportunity. Mowatt played a clever short corner to the near post which Conor Chaplin laid off to Brittain, but his goal-bound effort was flicked wide by team-mate Victor Adeboyejo.
Tuchel had set his side up in a 4-3-3 formation but, by the break, had no option but to effect a change. Antonio Rudiger and Reece James were brought on as Chelsea moved to a back four, and it had the desired impact as the eight-time cup winners held possession higher up the field and began to more regularly the test the opposing defence.
Abraham caught the ball under his feet on a promising counter and Hudson-Odoi flashed a shot across goal, before Rudiger had their clearest chance of the match so far from a Hakim Ziyech free kick but powerfully headed inches wide of the post.
But the momentum was finally with them and they would make it count. In the end it took one brutally swift move, Billy Gilmour releasing James who sprinted forward like lightening and squared the ball on a plate for Abraham to follow up his hat-trick in the previous round against Luton Town with another cup goal.
Barnsley, beaten 6-0 at Stamford Bridge in the EFL Cup earlier in the season, were never likely to lie down this time around and pushed forward with intent after the bitter blow. Of all their substitutes it was the defender Michael Sollbauer who came closest to a leveller, heading towards goal after Kepa failed to deal with a Mowatt free kick but seeing Abraham clear off the line.
Another sub, the debutant striker Daryl Dike, slipped as he attempted to fire in his only opening, and as the match moved into added time Michal Helik got the final chance to force another 30 minutes, but his header was saved by Kepa.
Fringe Blues fail to impress
With Andreas Christensen the only player to keep his place from Chelsea’s Premier League victory just down the road at Sheffield United last weekend, this was set up to be the ideal opportunity for the players who have less game time in the first weeks of Tuchel’s reign to make a positive impression.
In that regard, most failed miserably. While the choice of shape did them no favours, they failed to gain any foothold in the match in the first half, the midfield pairing of N’Golo Kante and Gilmour looking underpowered for the occasion.
The defence was put under near-constant interrogation by a Barnsley side which threw everything at them on and off the ball, and none of Emerson, Kurt Zouma and Christensen looked settled at the back, with the Dane hooked at the break alongside wing-back Marcos Alonso, who made very little impact in getting his team forward.
Only after the half-time changes in formation and personnel did Chelsea seem to have any sort of presence, but it was a regular in James who came off the bench and made the difference with one surging run and assist for Abraham, perhaps the only man in blue to make a step forward having failed to make it off Tuchel’s bench in the past two games.
Elsewhere the attacking talent in the squad failed to make any mark. Pulisic wasn’t at his freshest but still made very little happen when he did get on the ball, while Ziyech showed the odd nice touch but offered nothing creatively that was likely to trouble the opposition.
If Tuchel was hoping to see his options increase ahead of more crucial Premier League fixtures and the resumption of the Champions League, he will not have been encouraged but what he witnessed at Oakwell.
Young Reds continuing development
Barnsley have the youngest squad in the whole Championship and, under Ismael, they have developed into the most intense and – in the words of their boss – “unpleasant” teams in the division.
Their high press and direct play have seen a number of teams find themselves caged into their own third of the pitch at Oakwell, including Watford and Norwich City in the previous round, but to have Chelsea’s international stars in exactly the same predicament in the first 20 minutes was nothing short of extraordinary.
Keeping that intensity up for the entire match was never going to be possible, not that they ever stopped trying. But once Chelsea enjoyed some possession in their half they were always going to carry some quality threat, and so it proved with one quick, incisive move enough to win the match in the second half.
The biggest lesson for Barnsley is one that hardly needs repeating but remains no less true – you simply have to take your chances against these teams. Brittain had the biggest of them all, right in the middle of the six-yard box, and will long regret not directing it either side of Kepa. He also had a goal-bound effort denied by his own team-mate in that first half, while Sollbauer would have sent it to extra time if not for Abraham.
But for all the missed chances and what-ifs, this should be reflected on as a positive experience for them. They showed just how far their fight, energy and style of play can get them to unsettle one of Europe’s elite clubs, and will continue to be utterly fearless in the rest of the Championship season.
Man of the match: Tammy Abraham (Chelsea)
The difference-maker for the second round running, and needed to be with fewer chances coming Chelsea's way on a tough night. He made a telling contribution at the other end too by clearing off the line after his goalkeeper had gone AWOL.