Palace midfielder Danns fired home through a melee of players from the edge of the penalty area in the second minute and although the Londoners were unable to build on their advantage, the onus was on Leeds and it took Simon Grayson's side until the final 20 minutes before they rose to the challenge.
Leeds substitutes Sanchez Watt and Davide Somma both went close to snatching a point for the visitors, but it was too little too late and Palace, who had Danns sent off for two yellow cards in stoppage time, held on for victory.
Considering so much was hingeing on the result at Selhurst Park the tepid nature of the contest was baffling, but Palace were happy to merely contain their out-of-sorts visitors, who have secured only two points from their last five games and slipped to ninth place, three points adrift of the final play-off spot with two games remaining.
Palace escaped relegation on the final day of last season when a point from a 2-2 draw at Sheffield Wednesday was enough to send the Owls down at their expense, and they were never properly troubled by the Yorkshiremen.
Victory lifted Dougie Freedman's side up to 47 points, six better than nearest rivals Sheffield United with Palace holding a far superior goal difference.
Source: PA
Source: PA