The Spanish side, fresh from a 3-1 win over Newcastle United, made it back-to-back victories over Premier League opposition and it could it have been more convincing had Luis Alberto not missed from the penalty spot.
West Ham, who named a completely changed starting XI, needed a shoot-out to overcome the hosts in their tournament opener, and they were toothless in front of goal again, adding to manager Sam Allardyce's pre-season worries as his side remain winless in normal time.
Malaga scored twice in as many first-half minutes as Rescaldani and Luis Alberto found the net to put the Spanish outfit in control.
The Liverpool loanee spurned the opportunity to make it 3-0 when his tame spot-kick was saved by Adrian.
It was Malaga who made the brighter start, with Rescaldani flashing an effort wide of Adrian's goal after seven minutes following a dangerous delivery from recent signing Roberto Rosales.
Ricardo Vaz Te almost connected with Matt Jarvis' delivery soon after but Malaga took a firm grip on the game with two quickfire goals.
After Rescaldani had coolly side-footed home inside the area in the 23rd minute, Luis Alberto produced a fine finish when Juanmi's cross was not cleared by the West Ham defence.
The 21-year-old striker had a great opportunity to make it three from the spot after drawing a foul from debutant Carl Jenkinson, but Adrian denied him.
Luis Alberto thought he had doubled his tally when he had the ball in the net eight minutes after the break - only to be flagged offside - before Rescaldini and Pablo Perez forced Adrian into smart saves.
Arsenal loanee Jenkinson then gave Allardyce cause for concern when he was taken off after requiring attention from the physio.
The West Ham manager introduced youngsters Amos Nasha and Josh Cullen for a taste of the action in the second half ahead of his side's final friendly against Sampdoria on Saturday.