The 27-year-old, who had a short spell on loan with the Clarets four seasons ago, beat Nick Pope from the spot in the fourth minute after the England international goalkeeper was adjudged to have brought down the ex-Chelsea man.
Pope saved superbly from substitute Pablo Hernandez after the break, but it was Burnley who looked the most threatening in the second half.
The Clarets laid siege on Illan Meslier's goal - with Ashley Barnes testing the Frenchman twice - but the away side couldn't find a way through.
The Clarets laid siege on Illan Meslier's goal - with Ashley Barnes testing the Frenchman twice - but the away side couldn't find a way through.
.
Burnley's English manager Sean Dyche (L) and Leeds United's Argentinian head coach Marcelo Bielsa (R) shake hands ahead of the English Premier League football match between Leeds United and Burnley at Elland Road on December 27, 2020. Photo: Nigel French
. Nick Pope 7
Penalty decision was extremely harsh on Pope, who appeared to have made sufficient contact with the ball. Made routine saves from Rodrigo and Raphinha and later denied Hernandez with a wonderful fingertip save at full stretch. Photo: Nigel French
. Matt Lowton 6
Pulled from pillar to post when the home side worked the overload down his side of the pitch in the first half-an-hour, but settled into the game well. Neat and tidy in possession and got forward to support Burnley's attacks. Photo: Nigel French
. Charlie Taylor 8
Really confident on the ball and his calmness and assurance in possession took the sting out of the home side's spells of pressure. Darted forward time and time again, becoming one of the Clarets' most productive outlets. Photo: Oli Scarff
. James Tarkowski 7
Caught day-dreaming from Ayling's ball over the top, which led to the penalty. Other than that it was another typically dominant display at the back from Burnley's in-demand defender, who also carried a threat at the other end of the pitch. Photo: Nigel French
13. Dale Stephens 5
Provided Burnley with a bit more balance late on as they committed men forward in search of an equaliser. His introduction gave Brownhill the licence to push on as the visitors cranked up the pressure. Photo: Nigel French