Pinnock was on hand to provide the Reds with a timely boost as they saw off a Sunderland outfit who continue to struggle under recently-appointed boss Chris Coleman.
The Reds made a terrific start at the Stadium of Light.
The woodwork rescued the hosts when Mamadou Thiam lashed in a pile-driver from 25 yards that thumped the crossbar.
A minute later Adam Hammill met Joe Williams' cross, but could only divert a shot wide of goal.
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Sunderland responded with Callum McManaman forcing Adam Davies into a smart stop, then Saturday's late goal-scoring hero Ethan Pinnock was called upon to deny Lewis Grabban with a superb last-ditch tackle.
Back came the Reds, and Lloyd Isgrove produced a well-struck shot which Dutch 'keeper Robbin Ruiter did well to stretch and turn away for a corner-kick.
Brad Potts was proving a handful for the Sunderland defenders, and he came close to carving out a breakthrough when he scooped an effort over the top when under pressure.
There was a real let-off for Barnsley just before the interval as Bryan Oviedo's perfectly-execute free-kick curled around the defensive wall before striking the outside of a post.
The Reds drew first blood with a goal just two minutes into the second half.
Pinnock was the main man again, heading home Zeki Fryers' corner-kick at the back post.
Sunderland almost levelled minutes later, but Aiden McGeady's crisp effort curled inches past the post.
The Reds were in need of a potentially victory-clinching second goal, and they almost struck again when Potts was thwarted by a super save from Ruiter.
The hosts ought to have levelled again with 20 minutes left, only for Paddy McNair to somehow direct a shot off target from close range.
Sub Tom Bradshaw missed the Reds' best chance of grabbing a late second goal.
Sunderland (4-5-1): Ruiter; Matthews, Browning, O'Shea, Oviedo (Maja, 46); Love, McManaman (Asoro, 61), Gibson (McNair, 33), Honeyman, McGeady; Vaughan.
Subs not used: Steele, Jones, Beadling, Embleton.
Barnsley (4-3-3): Davies; Cavare, Pinnock, Lindsay, Fryers; Gardner (Moncur, 73), Williams, Potts; Isgrove, Thiam (Bradshaw, 73), Hammill (McCarthy, 90).
Subs not used: Townsend, McGeehan, Mallan, Ugbo.
Referee: Robert Jones (Merseyside).
Star man: Ethan Pinnock.