The Clarets fell 2-1 to Newcastle as Jesse Marsch's side managed the same score with a win at Brentford, which saw them leapfrog their rivals on a dramatic Sunday.
Sergi Canos was sent off for a second yellow as he removed his shirt after a 78th minute equaliser, following Raphinha's opener from the penalty spot.
But Jack Harrison then caused euphoria at the Brentford Community Stadium with his stoppage time long-range strike leaving Marsch a pile of joy on the touchline.
It was sheer misery at Turf Moor though, as two goals from Callum Wilson ended Mike Jackson's recovery job at Burnley, despite Maxwell Cornet's consolation hinting at a late turnaround.
The Clarets had survival in their own hands as they headed into the final day level on points with Leeds but with far superior goal difference, however Newcastle quickly put paid to that.
A blatant handball from Nathan Collins had gifted the Magpies the lead from the spot when Wilson tucked away in the 20th minute and he later doubled his tally with ease on the hour mark.
Burnley's stand-out star Cornet fired home soon after to give his side hope, but even an equaliser wouldn't have been enough as Harrison gave Leeds the win.
Instead of Cornet it was Leeds' star man Raphinha who was left celebrating, jumping in the crowd to enjoy the moment with the away fans.