Camacho headed home what would prove to be the only goal of the game in the seventh minute as Malaga followed up last weekend's home win over Getafe with another 1-0 triumph.
Elche's bid to get anything out of the game suffered a major blow in the 61st minute when they lost Damian Suarez to a red card and the hosts could not find a way to avoid a third successive defeat.
The result sees Malaga move up to four places to ninth on 20 points while last season's Segunda Division champions Elche remain three points further back.
Malaga finished fourth in 2012 and sixth last season but have struggled to build any momentum this term under new coach Bernd Schuster and came into Friday's game just four points above the relegation zone.
However, they received an early boost when, with their first serious attempt on goal, Camacho got on the end of Sergio Duda's curling free-kick to glance a header past home goalkeeper Tono and put the Andalusian side in front.
Elche tried to get back on terms before the break and almost managed it in the 36th minute when Ferran Corominas was denied by the feet of Malaga keeper Willy Caballero.
Carlos Sanchez also had a chance just before the interval but he could not turn in Edu Albacar's cross.
That was about as good as it was going to get for the home side, as they found themselves on the back foot in the second half, especially after being reduced to 10 men.
Elche survived a let-off in the 58th minute when Samu Garcia fired a good chance over from close range, but three minutes later the hosts were not so fortunate as right-back Suarez was handed his marching orders for a foul on the Malaga striker.
There was no way back for Elche after that and Malaga could have recorded a more comfortable win had Weligton, Francisco Portillo and Duda managed to convert their chances.