Former Burnley favourite Robbie Blake was given a mixed reception on his return to Turf Moor and was denied the opening goal of the afternoon thanks to an outstanding save from Brian Jensen.
Clarets boss Steve Cotterill was forced to reorganise his troops as Graham Branch fell victim to a crunching challenge from United's midfield enforcer Shaun Derry.
The home side went in front from the penalty spot on the hour after striker Ade Akinbiyi was pulled down by Sean Gregan.
Dead ball expert Garreth O'Connor scored from the resultant spot-kick with some ease. This was the fourth game running the Dubliner had found the back of the net.
Striker Blake should have equalised shortly afterwards but fired over the crossbar when only 15 yards from goal and then endured further frustration after a tantalising cross from the right evaded both the onrushing Rob Hulse and Lewis.
The American star Lewis equalised with a fine free-kick from the edge of the box, after Burnley left-back Jon Harley as the last defender, had only picked up a yellow card for pulling back Leeds substitute David Healy.
The winning goal was created by Lewis who skipped inside right-back Michael Duff and crossed for Hulse to head powerfully beyond the helpless Jensen.
The visitors were denied a third goal by the alert Jensen as Derry played a one-two with Lewis and seemed certain to score until the giant Burnley keeper intervened.
Leeds were indebted to a fine save from Neil Sullivan who denied Garreth O'Connor a second and equalising goal with an outstanding save.
After the game, police and stewards rushed up the tunnel after an alleged incident had occurred.