Koke opened the scoring at the Martinez Valero before the Colchoneros made the three points safe with a goal from the in form Brazil-born forward.
Koke opened the scoring midway through the second half and Diego Costa made the game safe for the Rojiblancos with 16 minutes to go.
Atletico had routed Getafe 7-0 in its previous Liga outing but struggled to break Elche down during a fiercely-contested first half.
However, Diego Simeone's men did have their chances, with Joao Miranda heading straight at Manu Herrera after being left unmarked at a corner 13 minutes in and Arda Turan firing just over the bar following a jinking run.
For the most part, though, Atletico failed to trouble the home side's defense, so it came as no surprise when former Barcelona striker David Villa was replaced by Raul Garcia just after the hour mark.
It was a bold move by Simeone but it paid off almost immediately, with Koke firing home a rebound after Herrera had failed to hold a strike from substitute Garcia.
Atletico sealed victory in the 76th minute when Costa finished clinically after being the recipient of the most wonderfully pin-point through ball from Adrian.
Elche tried to rally in the closing stages but to no avail, with Atletico ultimately cruising to a win that took the club to 40 points alongside league leader Barcelona, which faces a tricky trip to Basque country on Sunday to take on Athletic Bilbao.