The Championship outfit dominated proceedings and took a deserved lead when Polish defender Michal Helik headed in from close range just before the hour.
Cauley Woodrow made sure of victory in added time as he converted from the penalty spot to put Valerien Ismael’s side through.
Tranmere did have chances of their own and would regret some glorious opportunities in the first half which Kaiyne Woolery and James Vaughan couldn’t convert.
Story of the match
The action was end-to-end, albeit with the Championship side having most of the possession and chances. Conor Chaplin had two earlier sighters for them, firing into the side netting before demonstrating great control and finish only for the offside flag to be raised.
But some of the first half’s best chances fell to Tranmere, and they should have led when Otis Khan’s set-piece delivery ran to Woolery only for the winger to head straight at goalkeeper Brad Collins from close range.
Barnsley began to apply more pressure and some desperate defence was needed from Keith Hill’s men. Lee O’Connor came across brilliantly to block off Chaplin before George Ray made two interventions, denying Callum Styles and then clearing off the line from Dominik Frieser after Woodrow’s effort was sent spiralling by Scott Davies.
Woodrow also went close with a glancing header from a Frieser cross, but another big chance would come to Rovers before the break. Woolery was the creator this time as his great work down the flank led to a cross which Helik missed, but James Vaughan couldn’t find the corner with his effort as Collins blocked with his legs.
The visitors made a competitive start to the second half too, but the next chance they gave away would prove fatal. Barnsley were allowed to keep possession on the edge of the box following a corner and, after exchanging passes with substitute Luke Thomas, Herbie Kane floated in a cross which Helik powered beyond Davies for the defender’s fourth goal of the season.
Tranmere now needed to force the initiative but found it difficult to do so, and apart from a firm Woolery volley aimed just over the bar, they were creating little.
Instead they were frequently hanging on at the other end, with Ray denying Woodrow, O’Connor making a great challenge to stop Styles from tapping in a Callum Brittain cross at the near post, and Paul Lewis getting in the way of a Romal Palmer drive.
As they pushed in added time they were left exposed at the back, and the result was put beyond doubt at last when Jay Spearing fouled Thomas in the box and Woodrow converted from the spot.
Ismael’s perfect afternoon
Barnsley head coach Ismael described it as “a perfect afternoon” after seeing his very strong line-up do the business to reach the next round.
While they had to work for the win and needed just shy of an hour to take the lead, they dominated territory and possession and had 20 efforts in total, and never really looked like being pegged back once finally taking the lead.
But it was also a good day for other reasons, with two players coming off the bench for long-awaited returns. Toby Sibbick played half an hour in his first game of football for more than 11 months, having been out of favour under the previous management and failing to play at all on loan at Belgian side Oostende, while Jordan Williams featured for just a second time under Ismael following a recurring hamstring injury.
Those two defenders join two new arrivals at the club in the past week, centre-back Liam Kitching and striker Carlton Morris, who were made to wait for their debuts. Having got a settled team playing very effective football, Ismael will have more options to select from in the second half of the season.
Rovers fail to take chances
Tranmere were up against it from the beginning with a number of first-team regulars ruled out for injury and Covid-related reasons, including Sid Nelson, Callum MacDonald, Liam Feeney and Peter Clarke.
Despite the biggest absences being at the rear it was a tremendous display from the back four, particularly right-back O’Connor and Ray next him in the centre of defence, both of whom came into the team as beneficiaries of the misfortune of others.
That there was still only a goal in it going into the stoppage time was full credit to that backline, who remained solid in the face of considerable pressure and threw themselves at everything.
That effort might have earned Rovers more were it not for their inability to convert the big chances that they created. Woolery was a dangerous threat and Morgan Ferrier should promise, as did Khan with his set pieces, but without the finishing touch all their efforts would go without reward.
Man of the match: Lee O'Connor (Tranmere)
Although on the losing side, right-back O’Connor deserves huge credit for an immense defensive shift, as does Ray along side him the middle.