Armstrong’s 25th-minute spot-kick was followed up by a Tom Bradshaw brace as the Tykes sealed a memorable win against Steve Bruce’s charges – who visit St. James’ Park on Monday.
In League One, it was a frustrating evening for Alex Gilliead and Ivan Toney – neither of whom were able to record a win with their promotion-chasing sides.
Gilliead started and finished Bradford City’s 2-1 defeat to Fleetwood Town at Highbury Stadium, where the Bantams conceded twice late on, having led at the break.
Toney, meanwhile, was taken off midway through the second half as second-placed Scunthorpe United were held to a goalless draw by Walsall at Glanford Park.
Elsewhere, Macaulay Gillesphey racked up another 90 minutes as Carlisle United got their promotion bid back on track with a 2-1 win over Doncaster Rovers.
Gillesphey has been an ever-present for Carlisle of late, the Cumbrians still occupying an automatic spot in League Two with a third of the campaign remaining.
OUT ON LOANAdam Armstrong – Barnsley (end of season)Macaulay Gillesphey – Carlisle United (end of season)Alex Gilliead – Bradford City (end of season)Ivan Toney – Scunthorpe United (end of season)Paul Woolston – Blyth Spartans (work experience loan)Sean Longstaff – Kilmarnock (end of season)Callum Roberts – Kilmarnock (end of season)Freddie Woodman – Kilmarnock (end of season)Siem de Jong – PSV Eindhoven (season-long loan)Tim Krul – AZ Alkmaar (season-long loan)Kevin Mbabu – BSC Young Boys (season-long loan)Emmanuel Riviere – Osasuna (season-long loan)Henri Saivet – Saint-Etienne (season-long loan)Florian Thauvin – Marseille (season-long loan)