The Championship outfit started on the front foot and took the game to Chelsea as they looked the more threatening side.
With Barnsley throwing men forward and probing Chelsea's defense, they were presented with two glorious chances to break the deadlock. But the Tykes failed to capitalize and it was 0-0 at half-time.
Chelsea boss Thomas Tuchel, spotting his side’s frailties, made a double change as he switched to a four-man defense after starting with a back-three.
The Blues finally found the back of the net in the 64th minute through Tammy Abraham, with Billy Gilmour and Reece James combining well to set up the goal.
Barnsley came searching for an equalizer and were only denied by a brave goal-line clearance by Tammy Abraham, who nodded a goal-bound shot after Kepa Arrizabalaga strayed out to collect a corner kick.
In the end, the Blues did enough to hold on to their lead and keep a clean sheet. Chelsea will welcome Premier League strugglers Sheffield United to Stamford Bridge in the quarter-finals of the FA Cup.
Chelsea player ratings
Kepa Arrizabalaga 6.5/10
The Spaniard made his first appearance under new boss Thomas Tuchel and did well to keep a clean sheet. The Chelsea goalkeeper made a vital stop in the early stages to deny Callum Brittain from point-blank range.
Barnsley almost drew level when he was caught out following a late corner. However, Tammy Abraham made a brilliant goal-line clearance to head the ball to safety.
Emerson Palmieri 6/10
The Brazilian full-back struggled to perform in the wing-back role in the first-half, but found his mojo when he reverted to his natural left-back position. He struggled to play from the back but quickly snuffed out any danger when out of possession.
Kurt Zouma 6.5/10
The Frenchman was finally given a chance to impress Tuchel, and he did well. Zouma was solid in defense, making a game-high seven clearances, two blocked shots and two interceptions.
However, the centre-back allowed the Barnsley attackers to roam freely in the final third on a few occasions.
Andreas Christensen 6/10
The Denmark international struggled to play out from the back, as Barnsley’s energetic high-press caused him trouble.
At times, he was also caught out of position and lost the ball in dangerous areas. The Chelsea defender was hooked off just after the break as Tuchel opted for a back-four.
Marcos Alonso 5/10
It was a rather forgettable night for the Chelsea full-back as Marcos Alonso failed to make an impact on the left side for the Blues. He looked slow and failed to produce anything noteworthy before being substituted.
N’Golo Kante 7/10
Chelsea’s captain in the absence of Cesar Azpilicueta and Thiago Silva, the Frenchman made his first start under Tuchel. He impressed the Blues boss with his high energy levels as he kept running and covering ground in midfield.
However, due to his playing style, he was unable to dictate play or provide creativity in midfield.
Billy Gilmour 7.5/10
Chelsea’s academy graduate put on a show at the center of the park once more. He kept his passes simple and always looked to win the ball back whenever the Blues lost possession.
The Scottish midfielder played a key part in Chelsea’s winner, as he sent in a brilliant defence-splitting pass to the right-flank for Reece James to square it to Tammy Abraham.
Callum Hudson-Odoi 7/10
The Chelsea youngster started slowly but gradually grew into the game as the match progressed.
He constantly took the Barnsley defenders on and won fouls for his side.
Hudson-Odoi came close to breaking the deadlock after a brilliant solo effort, but his left-footed strike missed the target.
Another superb performance from a man who is gradually becoming a key part of Thomas Tuchel’s Chelsea.
Hakim Ziyech 5/10
The Morocco international was gassed at times and looked like a man struggling for fitness.
However, he made some brilliant plays, setting Hudson-Odoi free down the right-flank with a lovely one-touch pass. He also delivered a perfectly-weighted cross for Antonio Rudiger, who narrowly missed the target in the second-half.
Christian Pulisic 5.5/10
The USA international completed a few dribbles but failed to truly test Barnsley's defense. He continues to look a shadow of himself from last season and was hooked off in the second-half after failing to impact the game.
Tammy Abraham 8.5/10
In a Man of the Match performance, the striker grabbed the winner against a dogged Barnsley defense in the second-half. He also made a superb goal-line clearance to protect Chelsea's lead. Tammy Abraham truly delivered for the Blues at both ends of the pitch.
Player ratings of Chelsea substitutes
Antonio Rudiger 7/10
The Chelsea defender came on right after the half-time break as the Blues opted for a four-man defense. The towering centre-back was calm at the back and looked more assured than Andreas Christensen.
The Germany international also came close to scoring in the second-half, but his header was off target.
Reece James 7.5/10
An excellent second-half cameo from the Englishman. He provided Chelsea with the extra man in attack while also contributing brilliantly in defense.
He made an excellent run to meet Billy Gilmour’s searching pass, before galloping into the Barnsley box to square it for Tammy Abraham to tap in from point-blank range.
Tino Anjorin 6/10
The youngster replaced a struggling Hakim Ziyech in the 68th minute and showed flashes of quality.
Mateo Kovacic 5/10
The Croatian international came on for the final 10 minutes of the game and kept thing tidy to ensure Chelsea protected their lead.