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.
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.
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.
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.
