Ross McCormack put Leeds in front in the first half as the visitors looked to end their winless run, having arrived in Burnley without a victory in their last five games.
However Leeds had conceded nine goals in their last two games and could not hold on to the lead as a Jason Pearce own goal meant the teams went into half-time level.
And Arfield fired home a winner on 67 minutes to stretch Burnley's unbeaten league run to 14 games, with the Clarets still having not tasted defeat in front of their own fans in this Championship campaign.
After an even opening, Ross Wallace had the first chance of the match, cutting inside from the right before flashing his shot wide after five minutes.
The Clarets came close moments later when Dean Marney's trickery won a free-kick on the edge of the box - David Jones' subsequent effort curling narrowly over the bar.
Shortly after Leeds had a chance to open the scoring when McCormack sent through Matt Smith, whose effort was saved low by Tom Heaton.
A mistake from Jones then allowed McCormack clean through and the striker dinked over the on-rushing Heaton but saw his shot hit the post before Jason Shackell bravely blocked the rebound.
But on 27 minutes the visitors did take the lead as Smith superbly flicked on a Connor Wickham throw in to McCormack who powerfully headed past a helpless Heaton.
But Burnley responded on 38 minutes when Kieran Trippier found space on the right and delivered a cross that Pearce diverted past Jack Butland and into his own net.
Both sides began the second half with the same intensity that they finished the first with but it was Leeds who began to take a foothold in the match.
Their first real chance came when McCormack drilled in a cross from the right towards Alex Mowatt who miscued his shot before Smith fired over.
However, Burnley responded on 68 minutes when Ben Mee crossed from the left to Arfield. His first shot was blocked but the ball came back to him and he drilled home into the bottom corner.
The visitors still persisted and began to camp in the Burnley half as the game entered the closing stages.
And on 77 minutes Luke Murphy delivered a teasing corner but Smith and Pearce both failed to make clear contact from yards out.
In the last 10 minutes Burnley had a chance to make it 3-1 when Junior Stanislas crossed to Ashley Barnes but he could only head wide.
But it did not matter as the Clarets saw the game out to extend their unbeaten home run and compound Leeds' recent misery.