One of four teams to win their opening three matches along with champions Barcelona, Real Madrid and Villarreal, Atletico had far too much quality for the south-coast club on a festive afternoon for their fans packing a sun-bathed Calderon.
Villa, who joined from Barca in the close season, struck with a superb left-foot volley after a quarter of an hour and Diego Costa scored from the penalty spot, his fourth goal of the campaign, in the 37th minute to make it 2-0.
Rodri pulled one back for the visitors three minutes later before Tiago scored from a well-worked free kick in the 64th and Raul Garcia killed the game off in the 67th when he cleverly flicked the ball into the net from close range.
Atletico took their foot off the gas in the final minutes and Almeria winger Aleix Vidal swept into the area and beat Thibaut Courtois with a clinical shot in the 90th minute.
Atletico have won their opening four La Liga games for the first time since they last claimed the title in the 1995-96 season.
Barca host Sevilla later on Saturday (1800 GMT) before world record signing Gareth Bale makes his debut for Real Madrid in their match at Villarreal (2000).