The visitors named a much-changed starting line-up on Thursday, with manager Thomas Tuchel giving several fringe players an opportunity to test themselves.
A slow start to the first half saw both sides struggle to create, although the best chance of the opening 45 minutes fell the way of the hosts. Chelsea failed to clear their lines properly, allowing Callum Brittain to shoot at goal. However, Kepa was on hand to make a stunning save from point-blank range.
This proved to be the only goalmouth action of a largely forgettable first half but the visitors had two strong penalty appeals waved away.
The second half continued in the same fashion, with Chelsea controlling most of the possession but failing to make it count.
The visitors finally got the breakthrough in the 64th minute. A well-worked move allowed substitute Reece James to run down the right flank before teeing Tammy Abraham up in the box with a pin-point cutback.
The England striker made no mistake from six yards out to put Chelsea one goal ahead.
Despite some late pressure from the hosts, the Blues held on to secure a win in an instantly forgettable fixture.
The victory sees them book their spot in the last eight, where they will take on Sheffield United for a place in the semi-final.
Here are five talking points from the fixture.
#5 Impressive Barnsley push Chelsea to the limit
There were 27 places on the English league hierarchy between Chelsea and Barnsley coming into this fixture.
Despite the gulf in class, the Championship side held their own against their more illustrious opponents.
The capital side expectedly had more of the possession, with Barnsley having just 27% of the ball. The hosts, however, made every second of it count and fashioned more chances than the Stamford Bridge outfit.
In total, they had 14 shots to Chelsea's six, four of which were on target, compared to one for the visitors. Furthermore, they had seven corners compared to Chelsea's two. The hosts can count themselves unlucky not to have gotten on the scoresheet.
In many ways, Barnsley were the better side on the night. Although Chelsea secured a much-needed victory, Valérien Ismaël's men can hold their heads high after what was a convincing performance.
#4 Fringe players fail to take opportunity
Thomas Tuchel is barely two weeks into his tenure as Chelsea manager. As such, his preferred starting line-up cannot exactly be inferred yet.
However, the German tactician had shown his hand in his first four games in charge, and a comparative list of starters could be drawn from the teams he named.
The clash with Barnsley saw Tuchel hand rests to several players who have featured regularly under him. Opportunities were given to others who had not been afforded much playing time.
This was an opportunity to state their case and give the manager selection headaches, but most of the players hardly did their cause a world of good.
The likes of Hakim Ziyech, Christian Pulisic, and Billy Gilmour were largely anonymous against lower division opposition.
With opportunities to impress coming at a premium for several of Chelsea's players, the Barnsley game offered an excellent opportunity to show what they are capable of.
They, however, failed to take it, which might make Thomas Tuchel's selections much easier in future.