Denmark defender Andersen turned a Matty Cash cross into his own net after 27 minutes and there was little sign of a fightback from Patrick Vieira’s side even before six minutes of madness from Cheick Doucoure saw him dismissed for two yellow cards early in the second half.
Unai Emery’s first victory over Palace keeps a Villa side once with relegation worries of their own in touch with the European battle, but though only one place separates these two clubs in the table it is a very different picture for Vieira.
The Frenchman insisted this week he does not fear the prospect of a relegation battle but he surely should as his side’s winless 2023 continued, leaving them only six points clear of the bottom three.
Defeat made it nine league games without victory, and with Manchester City, high-flying Brighton and Arsenal up next, things could soon get worse.
The recent absence of Wilfried Zaha has only added to Palace’s shortcomings given their dismal 10 per cent win record without him since the start of last season.
It looked as though their talisman’s return from a hamstring injury could solve both problems as he had the ball in the net with less than five minutes gone.
But Zaha was fractionally offside as he raced on to Ebere Eze’s ball from the left before he rounded Emiliano Martinez to apply the finish, and the goal was ruled out after a lengthy VAR check.
Having survived that let off, Villa grew into the game. Ollie Watkins got slightly in John McGinn’s way as he stooped to meet Alex Moreno’s cross, flashing a header wide.
But McGinn then set up the Villa goal, threading a pass into the path of Cash as he charged down the right. Cash sent in a low ball for Watkins, but Andersen got their first, sliding in to clear but instead diverting the ball past Vicente Guaita.
Palace’s attacking intentions continued to be frustrated by the offside flag as they struggled to create opportunities, and it was Villa who should have added to their lead before the break.
Emiliano Buendia’s pass picked out Watkins who wriggled free inside the area, only to place his shot the wrong side of the post.
There had been little sign of Palace getting back into the game in the early part of the second half, and hopes would be all but extinguished just after the hour mark.
Doucoure was book for a challenge which ended Boubacar Kamara’s afternoon in the 56th minute, and when he then left Kamara’s replacement Calum Chambers in a heap with another late tackle moments later, Craig Pawson produced a second yellow card.
Zaha did his best to provide some inspiration for Palace, wriggling free of three defenders before bending a shot wide, though it may not have counted due to the use of a hand when he momentarily slipped.
It said much about the game that neither side had a shot on target until the 74th minute, when Guaita did well to keep out McGinn’s shot from close range as he met substitute Leon Bailey’s low cross.
McGinn had another glorious chance in the 84th minute as Chambers led a charge down field and the ball was cut back for the Scotsman in space on the penalty spot, but he took too long to pull the trigger and his shot was charged down.