Villa, now without a point in four games, are rapidly being dragged into the relegation dog-fight.
They battled hard and were worthy of a point for their determined attacking play in which Gareth Barry and Mustapha Hadji produced their best individual performances of the season.
Beckham, however, demonstrated his danger to Villa as early as the first minute when he produced a goalbound effort following a cross from Ole Gunnar Solskjaer.
But his close-range effort was blocked by Stefan Postma who had taken over from Petr Enckelman.
The danger down the left was always evident as Ryan Giggs was given a great deal of room by J Lloyd Samuel.
Villa replied with a low cross shot from Hadji but there was little conviction about Villa's attacks.
This was in sharp contrast to United's attack. Villa's defence was far from confident as illustrated when Beckham scored the opening goal after 11 minutes when he turned in a Giggs cross despite the close attention of Alan Wright.
Barry emerged as Villa's key player with some delightful play.
One Barry cross was headed just wide by Dion Dublin, while on another occasion he sent Darius Vassell racing clear of United's defence with a perfectly-weighted pass.
Vassell raced into United's area but Fabien Barthez narrowed the angle and pushed away the striker's low shot for a corner.
Beckham, meanwhile, was extremely fortunate not to collect a yellow card for a trip on Barry.
In the swirling wind ball control was always difficult and Barthez was completely beaten by a powerful effort from Hadji which whistled just wide of the post.
A minute later Barthez was beaten by a Hadji header which crashed onto the back netting as United survived some blistering Villa attacks.
There was another let-off for United at the start of the second half when Hendrie carelessly blasted his shot over the bar to highlight his own miserable match performance.
Barthez again excelled when he saved a well-directed header from Dublin and then finger tipped a shot from Wright over the bar.
The response from United was a free-kick from Giggs which rammed against the angle of the bar as the Old Trafford side maintained their slender lead to chalk up another valuable away win.