Sky Blues defeated at Oakwell, with Stuart Beavon on target for Mark Robins' side...
City started brightly, with Jodi Jones' pace causing problems in the early exchanges. Liam Kelly's through ball found the wideman, but Nick Townsend was on hand to deny Jones, with McNulty and Beavon having efforts blocked on the rebound.
The home side looked threatening coming forward, but were being reduced to efforts from long-range, with George Moncur and Stevie Mallan denied by comfortable Lee Burge saves.
Barnsley took the lead midway through the first half, with Burge this time unable to deny Mallan. The midfielder picked up the ball inside the area and fired an effort into the top corner from a tight angle to give the Tykes the advantage.
The Sky Blues responsed well and would have been level if not for a fantastic save from Barnsley 'keeper Nick Townsend. Jones burst forward, cutting inside onto his left foot and curling an effort towards the top corner, but the shot stopper tipped it round the post.
Barnsley doubled their lead five minutes before half time with the impressive Jason McCarthy forcing a good save from Burge, before Stefan Payne had the simpliest of finishes from the rebound.
The Sky Blues made one change at half-time, with Ben Stevenson coming on for Liam Kelly in the centre of midfield. It was the midfielder's intial ball that set-up a chance for Stuart Beavon.
The striker pounced on a loose touch in the Barnsley defence to bundle his way through and calmly finish over Townsend to reduce the deficit to just the one goal.
However, the two-goal lead would soon be re-established, as Tom Bradshaw bundled home from close-range, pouncing on a lovely ball from Lloyd Isgrove across the six-yard box.
Coventry City: Burge (GK) (O'Brien 55'), Grimmer (Di. Kelly-Evans 68'), Willis (Hyam 73'), McDonald (Trialist 73'), Leahy (Maycock 73'), Kelly (Stevenson 45'), Doyle (C) (Shipley 68'), Jones (Trialist 68'), McNulty (Ponticelli 55'), Vincenti (Dev. Kelly-Evans 68'), Beavon (Biamou 55').
Barnsley: Townsend (GK), McCarthy, Jackson, Pinnock, Fryers, Isgrove, Moncur, Mowatt, Mallan, Payne, Brown.
Barnsley Subs: Davies (GK), Walton (GK), Yiadom, MacDonald, Lindsay, Hammill, D'Almeida, Bird, Ugbo, Bradshaw.