The United manager, aiming for a top-six place by Christmas, had been slammed by angry fans expecting a quick return to the Premier League.
But after securing just one win in their last seven home games, the Blades were indebted to Kilgallon who grabbed his first goal for the club since his £2million move from Leeds 11 months ago.
United, hoping to bounce back after two straight defeats, almost took the lead in the ninth minute when midfielder Nick Montgomery surged into the area tracked by Brian Howard.
The Barnsley skipper lunged in from behind as referee Phil Dowd waved away United's appeals for a penalty.
United, playing the more direct football, pressed again, midfielder Michael Tonge drilling in a long-range strike that was safely snuffed out by Heinz Muller.
Minutes later the German keeper stuck out a foot to deflect Phil Bardsley's low drive as the Blades turned the screw.
A stinging Keith Gillespie free-kick was hacked clear of the packed goalmouth, Kilgallon saw his low strike curl wide of the far post and Montgomery's looping cross almost dropped in at the far post as Muller scrambled back.
Barnsley carved out their first effort on goal ten minutes after the break, Martin Devaney picked out Jon Macken. The little striker headed the ball back to Istvan Ferenczi but Paddy Kenny produced a reflex save to keep out the lanky Hungarian striker.
United snatched the lead in the 64th minute when the under-pressure Barnsley back four were unable to keep out Gillespie's free-kick and Kilgallon steered the ball past the sprawling Muller from six yards.