Mateusz Klich curled in from the edge of the penalty area shortly before half-time and Jack Harrison’s flicked finish from Ezgjan Alioski’s strike after 60 minutes all but sealed the three points.
Substitute Rodrigo scored twice in three second-half minutes to complete a fine away win, producing a delightful chip over Bailey Peacock-Farrell for his first before rounding the Clarets keeper for Leeds’ fourth.
The result means Leeds have lost only once in nine league games and remain on course for a top-half finish – if not a late push for European football.
Burnley confirmed their Premier League safety with victory over Fulham on Monday and had made a promising start, but Charlie Taylor produced an excellent sliding block to deny Raphinha and the Brazilian also attempted an instinctive over-head strike prior to Klich’s opener.
Matej Vydra was thwarted by the outstretched leg of Illan Meslier as Burnley pushed for an equaliser, before the visitors’ dominant end to the contest ensured Burnley remain 15th.
Leeds are ending their first Premier League campaign in 16 years in great form and, though they began second-best on Saturday, Bielsa’s side showed their class in a dominant second-half display.
Bamford had gone closest in the opening stages as he forced Peacock-Farrell into action, before Klich ended Burnley’s resistance before the interval with an unopposed run and fine finish into the bottom corner.
With England midfielder Kalvin Phillips back to handle the physical test posed by the hosts and the flare of Raphinha reinstated in attack, Leeds were able to cut loose in the closing stages despite a quiet afternoon for top scorer Bamford.
Rodrigo replaced Bamford – who was unable to further his case for an England call-up – before the hour mark and it proved an inspired move as a tiring Burnley were unable to live with the sharp movements of the £26m summer signing from Valencia.
But Harrison, 24, was arguably the standout performer as he claimed a goal as well as two assists for Rodrigo – leaving only Manchester United’s Bruno Fernandes with more goal involvements from midfield in the Premier League this season.
