The Reds are through to the next round of the Carabao Cup with a decent performance in the north east against Middlesbrough.
First half strikes within 10 minutes of each other saw the Reds through here at the Riverside in the Carabao Cup.
Patrick Schmidt and Jordan Williams with the crucial goals on a ridiculously hot evening on Teesside.
It was a much-changed starting lineup selected by Gerhard Struber for this one, with a debut in defence for Michal Helik, a full debut for Dominik Frieser up front and a return to the starting XI for goalkeeper Brad Collins.
Also picked to start were Luke Thomas and Patrick Schmidt and both were heavily involved in a bright first half for the Reds who were wearing the changed yellow kit for the first time this season.
But it was our hosts who first tested their luck, when after a scrappy opening to proceedings, midfielder Lewis Wing twice tried from outside the box to beat Collins, with one effort going well wide and another fired straight into the Reds' stopper's hands.
On 10 minutes the Reds had their first glimpse of goal when Kilian Ludewig flashed a low cross into the middle of the box that Frieser hit first time, but couldn't direct it beyond Marcus Bettinelli in the Boro goal who saved low down at his near post.
Barnsley deservedly went ahead in the 22nd minute when some fluid and intricate passing from left to right ended with Thomas finding Schmidt inside the area, 12 yards out to the right and he found the near corner after giving the 'keeper 'the eyes'.
It was 2-0 around 10 minutes later as another fine move down the left saw Thomas play in Jordan Williams inside the box and to the left, and the rampaging full-back fired in at the near post to double the Reds' lead.
HALF-TIME: Boro 0-2 Reds
It was a much scrappier second period, where the home side looked for a way back into the tie against a resolute Reds rearguard.
Some great aerial defending from the back three of Sollbauer, Andersen and new man Helik repelled the Boro fightback.
Cauley Woodrow was introduced on the hour-mark, replacing Thomas who'd done much of the first half damage.
Schmidt nearly grabbed his second goal when he latched onto Mowatt's delicious through-ball, but his powerful drive was parried away by Bettineli.
Sollbauer was replaced by Aapo Halme soon afterwards, with the big Finn in the referees notebook a little while later for an innocuous challenge in midfield.
Brad Collins had to touch over a late free-kick from Paddy McNair but other than that, it was fairly comfortable for Struber's side who now head to Stamford Bridge and Chelsea in the last 32.
FULL-TIME: Boro 0-2 Reds
Collins, Ludewig (Styles), Sollbauer (Halme), Helik, Andersen, J.Williams, Ritzmaier, Mowatt, Thomas (Woodrow), Schmidt, Frieser.
Unused: Walton, Miller, Adeboyejo, Chaplin.