The visitors scored twice in quick succession in the first half through Manu del Moral and Fidel Chaves, but Jorge Molina's goal put Pepe Mel's side back in contention before the break.
Dominga Cisma was sent off one minute into the second half for a second yellow card but, even with an extra player, Betis' search for an equaliser proved elusive thanks in no small part to the heroics of Elche goalkeeper Manu Herrera.
The game took a while to get going, with the first shot from either team only arriving after 17 minutes when Betis midfielder Juan Matilla hit an effort over the bar.
Matilla then had a shot blocked by an Elche defender following smart footwork by Salva Sevilla in the box and the hosts thought the block was with a hand, but their loud appeals could not convince referee Carlos Velasco Carballo.
Elche took the lead against the run of play with just under half an hour played. Cisma cut inside from the left and delivered a short but accurate cross to Del Moral, who headed into the bottom corner.
The goal was more painful for the hosts given that Del Moral is on loan at Elche from Betis' fierce local rivals Sevilla.
The second came just a few minutes later. Coro ran on to a long punt up field and held the ball up patiently inside the area before laying it off to
Fidel, who took one touch before shooting into the bottom corner.
Herrera produced an outstanding save from Juan Carlos to prevent the hosts getting a quick goal back, but they were soon allowed back into the game when Molina headed home a free-kick from Salva Sevilla, despite being offside when the ball was played.
Molina was inches away from getting an equaliser midway through the second period but Herrera came out to block his close range shot, which rebounded off the goalkeeper and back off the striker but just wide of the near post.
Herrera would continue to be a thorn in Betis' side as the game went on, later tipping over a chip from Molina and then plucking a cross from Juan Carlos out of the air to avert the danger.
Sergio Mantecon was presented with a chance to kill the game off with seven minutes remaining as he raced towards goal unchallenged on the counter, but his poorly-struck effort was kicked away by Betis goalkeeper Guillermo Sara.
In the final minute, Betis defender Paulao headed a cross on to the post but the flag had been raised for offside.
Elche move up to 10th in the Primera Division table, while Betis slip down to 15th.