The home side opened the scoring with only six minutes gone when Kevin Gameiro poked home from close range.
Almeria were level, however, when Rodri chipped his effort into the back of the net from close range.
Sevilla could have regained the lead but Bryan Rabello saw his volley smash off the crossbar.
Jairo Samperio was next to threaten but after breaking into the Almeria box, he shot wide.
Rakitic had an opportunity with a 30-yard free kick, but his shot was poor and went well over the bar.
Jairo pushed forward again in search of a goal but found Esteban in good form.
Summer signing Vicente Iborra came close to finding the bottom corner but again Esteban was there to save.
However, Rodri almost got his second moments later, but his volley was kept out by Beto at point-blank range.
With time running out, Rakitic turned in Marko Marin's cross to steal the win.