Mateusz Klich fired a dominant Whites in front with a beautiful curled finish from the edge of the box in the 44th minute.
Jack Harrison's clever flick then doubled the advantage on the hour mark and substitute Rodrigo then netted twice in quick succession after two superb assists from Harrison in the 77th and 79th minute.
Burnley began brightly and Josh Brownhill sent an effort wide from the edge of the box as the opening exchanges were played almost entirely in the Clarets half.
Leeds fashioned their first opening in the tenth minute when Klich played in Patrick Bamford whose low drive from a tight angle was saved by former Whites 'keeper Bailey Peacock-Farrell.
Stuart Dallas then fired over on the turn before seeing another shot deflected wide as the Whites cranked up the pressure.
The Whites then squandered their best chance yet on the half hour mark as a Kalvin Phillips cross picked out Pascal Struijk who sent a firm free header just wide.
A lovely move then set up a fine opportunity for Gjanni Alioski who sliced his effort out for a throw before an acrobatic volley from Raphinha from a rapid break was sent over the bar.
But Leeds finally went ahead in the 44th minute when Klich led another attack with a run through the middle before sending a lovely curled finish into the bottom right corner from the edge of the box.
Burnley began the second half brightly and Westwood smashed a long range half volley wide.
The Clarets should have equalised in the 55th minute when Matej Vydra raced clear one on one but Illan Meslier produced an excellent save.
Wood then fired over but the Whites doubled their lead on the hour mark when Harrison produced cheeky flick to send a low drive from Alioski beyond Peacock-Farrell.
Back came Burnley as Westwood sent another effort wide and Meslier then saved the day once more with a strong save to keep out Jóhann Berg Gudmundsson after he was played in.
And just moments later Leeds bagged their third as fine pass from Harrison played in substitute Rodrigo who produced a lovely turn and precise lobbed finish to beat Peacock-Farrell.
Leeds were cruising and the Whites added a fourth just two minutes later as Harrison again played in Rodrigo who rounded Peacock-Farrell before firing into an empty net.
Burnley had chances to pull a goal back and James Tarkowski sent an effort just over the bar.
Rodrigo then squandered a chance to complete a rapid hat-trick when firing just wide but Leeds were already home and dry and netted a 16th Premier League win of the season in style.
Burnley: Peacock-Farrell, Lowton, Tarkowski, Mee, Taylor; Brownhill, Westwood, Cork, McNeil (Gudmundsson 70), Vydra (Rodriguez 66), Wood (Barnes 66). Subs not used: Norris, Nartey, Dunne, Pieters, Richardson.
Leeds United: Meslier, Ayling, Llorente, Struijk, Alioski, Phillips, Klich (Roberts 76), Dallas, Harrison, Raphinha (Poveda 81), Bamford (Rodrigo 58). Subs not used: Casilla, Cooper, Davis, Berardi, Jenkins, Shackleton.
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Thank you Laura Collins