Ultimately, though, Roy Hodgson's pacy side caused problems throughout the contest as Leeds followed Monday's 4-1 defeat at home to Leicester City with another loss by the same score.
Palace took the lead in the 12th minute when Scott Dann rose above both Liam Cooper and Robin Koch to connect to a corner with the ball beating Illan Meslier in off the bar into the top right.
Leeds looked to have drawn level just four minutes later when a majestic through ball from Mateusz Klich played in Bamford who neatly chipped home yet the goal was chalked off after a VAR check for offside with Bamford's hand judged to be offside.
Salt was then rubbed into the wound when Eberechi Eze converted an outstanding free-kick from the edge of the box into the top left corner that went in off the bar in the 23rd minute after Koch fouled Eze for the foul.
Leeds, though, hit back with a goal that finally stood in the 27th minute when Klich's flicked header set up Bamford who brilliantly cushioned the ball before finishing with a clinical volley for his seventh goal of the season in the 27th minute.
United's response had been admirable but Palace then restored their two-goal lead with a freakish own goal three minutes before the break as a cross from Patrick van Aanholt took a deflection off Helder Costa to somehow beat a stranded Meslier from an angle of eight degrees.
Summer recruit Raphinha replaced Costa during the half-time break and Leeds went close to pulling a goal back in the 51st minute when Pascal Struijk sent his header wide from a corner.
From a rapid Whites counter, Gjanni Alioski then saw his effort from the edge of the top tipped wide and from another fine move Jack Harrison's firm effort was safely held by Vicente Guaita.
Wilfried Zaha then failed to beat Meslier from inside the area after being set up by Jordan Ayew but Leeds were threatening and an Alioski cross flew across the Palace box.
But gaps were being left at the back and Zaha then easily picked out Ayew inside the box and the Palace striker squeezed a shot past Meslier that hit the net in off the post in the 70th minute.
A potential Bamford chance of a header than hit the Whites striker's shoulder and Palace went close to adding to a fifth with van Aanholt denied by Meslier before volleying wide.
The bright Raphinha also fired a smart free-kick just wide as Leeds looked to attack until the end but the contest had long since been settled as United's dreadful run in London continued.
The Whites have not won in London since the 3-1 victory at QPR in December 2017 and United now sit 14th in the Premier League table after eight games played.
Crystal Palace: Guaita, Clyne, Kouyaté, Dann, Van Aanholt, Townsend (Schlupp 71), McArthur, Riedewald, Eze, Ayew, Zaha. Subs not used: Butland, Sakho, Cahill, McCarthy, Schlupp, Benteke, Batshuyai.
Leeds United: Meslier, Ayling, Koch, Cooper, Dallas, Struijk (Roberts 71), Klich, Costa (Raphinha 46), Alioski, Harrison, Bamford. Subs not used: Casilla, Poveda, Davis, Jenkins, Casey.
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Thank you Laura Collins