The Tykes, in fourth-bottom spot, rose to 32 points thanks to their point in a 1-1 draw against the fifth-bottom Tigers.
Oli McBurnie, who opted to join Barnsley on loan from Swansea in January despite interest from Sunderland, put the Oakwell men in front, but experienced centre-back Michael Dawson rescued Hull with a 73rd-minute leveller.
Sunderland, with 12 games to go, are bottom on 27 points, joined in the drop zone by Burton Albion (29) and Birmingham City (30).
Barnsley have 32 points, and a much superior goal difference compared to the three sides below them, with Hull one point better off, on 33. Bolton are on 34 points alongside Reading, who were beaten 3-1 at home by Sheffield United tonight.