Azeez drilled a strike from 30 yards in only the third minute which beat the Betis defence in the only breakthrough of the game.
The result means Almeria climbed out of the bottom three and into 15th place while Betis remain rooted to the bottom of the overall standings.
After Azeez got the visitors off to the perfect start, Ruben Castro tried his luck from the middle of the area only to be denied by Marco Torsiglieri before Javier Matilla tested Almeria keeper Suarez Esteban with a fantastic strike from 25 yards.
Azeez forced a save from Guillermo Sara in the 36th minute, with the Betis keeper tipping his 25-yard strike round the post, before the action switched to the other end moments later when Juan Carlos was denied what would have been a 30-yard curling effort by Esteban.
Sara saved another good strike from Almeria's Oscar Diaz in the 41st minute before Jorge Molina Vidal fired a chance over the bar for the home side.
Despite the flurry of chances, Almeria kept their slender lead at the break, and the second half picked up where the first period had left off when Alvaro Vadillo's effort from the edge of the box was caught by Esteban.
Molina also hit his next strike directly at the keeper and Esteban saved a strong strike from Javier Matilla in the 70th minute to preserve his side's advantage.
Diaz blazed over the bar moments later at the other end in what was Almeria's last real chance of the match, with Nono's late strike from distance denied by the solid Esteban two minutes from the final whistle.