Barnes, recalled in place of Marvin Sordell by Sean Dyche, headed home the decisive goal at Turf Moor early in the second half after sloppy defending from the visitors.
In a first half lacking genuine quality, the hosts came closest to breaking the deadlock through a Danny Ings shot, while Robbie Brady had to be on hand to clear off the line.
Barnes' header put Burnley into a deserved lead and forced Hull to raise their game, although the visitors' efforts in attack routinely ended in frustration and they ended the game having mustered just one effort which forced home goalkeeper Tom Heaton into action.
Curtis Davies' back injury completed a miserable day for Steve Bruce, the central defender forced off late in the game, leaving his side with 10 men.
Despite winning at the 11th time of asking, Dyche's men are still at the foot of the table, while Hull remain only two points above the bottom three.
Steve Harper, one of two changes for the visitors, was tested twice by Ings in the opening 20 minutes, but the experienced goalkeeper stood firm on his return from a torn bicep.
Harper's second save was almost undone as Paul McShane sliced the loose ball towards his own goal, but Brady was able to clear off the line.
After a first half devoid of clear goalscoring chances, the hosts showed renewed spirit after the break and opened the scoring in the 49th minute.
Kieran Trippier delivered a deep cross into the penalty area, and Barnes got in front of Ahmed Elmohamady to fire a bullet header past Harper.
Abel Hernandez failed to convert Elmohamady's cross soon after, while Bruce introduced Gaston Ramirez, Stephen Quinn and Hatem Ben Arfa as Hull looked to get back into the contest.
The decision to make all three changes quickly backfired on Bruce as Davies' attempts to execute an overhead kick saw him suffer a back injury.
Davies landed heavily and tried to carry on for a period after treatment, but was ultimately forced off with 20 minutes remaining, forcing Hull to reshuffle their defence as attack remained a priority.
Hernandez headed straight at Heaton before controlling an Elmohamady pass on his chest and turning neatly, but his effort from the edge of the area zipped wide of the left-hand post.
As the visitors' spirit dwindled, Burnley went closer to scoring the game's second goal in the closing stages, ultimately holding on for three points which will give eternal optimist Dyche plenty to enjoy.
