Ali Houary opened the scoring at the Pinatar Arena after 22 minutes and Umaru Konare Tounkara doubled the lead for the Spanish side on the stroke of half time.
Asanele Velebayi netted his second goal of pre-season as he found a 58th minute consolation goal.
It may have been worse for the South African side but Brandon Petersen made an 83rd minute penalty save.
Amakhosi kicked off their pre-season tour with a 1-1 draw with Scottish side Rangers before being held to a 1-1 draw with Al Kholood from Saudi Arabia.
They had a superb chance to take the lead in this match but Flavio Da Silva was unable to get his head to a superb Thabiso Monyane cross.
Chiefs then found themselves behind to a mazy run and low shot that beat Petersen in the Amakhosi goal.
Tounkara headed a second goal home from close range, and despite Elche being in control for much of the tie, Lebohang Maboe did well to break forward and tee up Velebayi for a deserved tap-in.
Velebayi had netted his first goal of pre-season in the 1-1 draw with Al Kholood.
Chiefs next face Zimbabwean champions Scottland FC in the 2026 Toyota Cup on Sunday, 26 July.