Almeria took an early lead through Fernando Soriano only for Edu Albacar to equalise from the spot following Sebastian Dubarbier's handball.
The hosts regained the lead on the stroke of half-time when Jose Antonio Verza converted a spot-kick following Cristian Sapunaru's handball.
Almeria appeared to be heading for victory, despite Dubarbier's second-half dismissal after receiving his second yellow card, before Boakye struck to leave both sides searching for their first win.
The hosts almost went ahead in the ninth minute in spectacular style when Soriano's 35-yard shot was tipped round by the post by Herrera Manu.
However, they did not have to wait long to take the lead as they went ahead just a minute later when Ramos Rafita's cross from the right was headed into the bottom left-hand corner of the goal by Soriano.
Elche had not shown at all as an attacking force when they were gifted an equaliser as Dubarbier handled in the box and Albacar powered the resulting penalty home 12 minutes before the break.
Suso shot wide for Almeria while home goalkeeper Suarez Esteban saved Ferran Corominas' header and it appeared the game was heading for the break all-square.
However, in injury time, the hosts were themselves awarded a penalty for handball, this time by Sapunaru and Verza slotted the ball into the bottom right-hand corner of the goal.
Verza started the second half where he had left off and Manu was called upon to tip his close-range shot round the post.
Elche responded with Sapunaru's header comfortably gathered by Esteban and Ruben Perez del Marmol firing wide.
The visitors were given a boost when Almeria were reduced to 10 men, Dubarbier sent off in the 67th minute for his second bookable offence when he fouled Boakye.
The striker then came close, his shot from the right of the area parried by Esteban with Niguez Aaron firing straight at the keeper moments later.
It was all Elche now and Almeria were grateful to Esteban after he tipped Corominas' shot round the post.
The game had moved into injury-time when Ruben Perez's shot was comfortably gathered as Almeria appeared to be heading for their first win before Boakye's intervention as he slotted home Corominas' pass into the bottom left-hand corner of the goal.