Fran Escriba's hosts had the better of the opportunities to force an opener in the first half but their opponents gave as good as they got.
The draw extended Betis' unbeaten run to five games in all competitions, leaving them nine points from safety, while the point moves the hosts up one place to 13th.
Both sides took a while to get going and it was Elche that had a the first real chance of the game as Ruben Perez powered a great shot from just outside the box - forcing Antonio Adan to punch the ball to safety.
After 17 minutes the visitors lost former Espanyol defender Didac Vila to an injury and he was replaced by Jose Caro, making just his second league appearance of the year.
It was not until just after the half-hour mark that the visitors had their first chance to get on the scoresheet but Ruben Castro's weak effort was comfortably caught by Elche goalkeeper Manu Herrera.
Betis then lost substitute Caro to injury five minutes before the break and the 21-year-old was replaced by Antonio Amaya at the back as Gabriel Calderon was forced into his second change of the match.
Castro almost handed the away side the lead as the game approached half-time but his long-range effort sailed over the bar before Salva Sevilla's free-kick was punched to safety by Herrera.
The home side came out stronger for the second half and Ferran Corominas could have broken the deadlock, but Amaya was quick to block.
Javi Marquez was next to have a go at the Betis goal before he sent his long-range volley over the crossbar as Elche continued to press forward.
The hosts lost Manu Del Moral to injury just before the hour mark and he was replaced by on-loan Levski Sofia striker Garry Rodrigues, moments before Cristian Herrera's close-range attempt flew over the bar.
Cedrick drilled a shot past the Elche goal as the game wore on and both sides battled to find a goal and Perez almost stole victory for the home side in the dying minutes but he mishit the ball from the left of the penalty box and sent it wide of the target as the points were shared.