Pinnock was on hand to provide the Reds with a boost as they saw off a Sunderland outfit who continue to struggle under recently-appointed Chris Coleman.
The Reds made a terrific start at the Stadium of Light - 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.
Sunderland responded with Callum McManaman forcing Adam Davies into a smart stop, then Saturday’s late goal-scoring hero Pinnock was called upon to deny Lewis Grabban with a last-ditch tackle.
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Back came the Reds, and Lloyd Isgrove produced a well-struck shot which Robbin Ruiter did well to 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.
There was a real let-off for Barnsley as Bryan Oviedo’s perfectly-execute free-kick curled around the defensive wall before striking the outside of a post.
The Reds scored two minutes into the second half. Pinnock headed home Zeki Fryers’ corner-kick at the back post.
Sunderland almost levelled, but Aiden McGeady’s crisp effort curled inches past the post.
The Reds 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.
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).
Att: 28,311