The striker hit a sensational volley after 61 minutes, finally converting one of the numerous chances that had fallen at his feet during the game, although once again Joaquin Caparros' side were grateful to their goalkeeper Keylor Navas, who produced an outstanding save to prevent a late equaliser from Oscar Diaz.
Levante have now gone six games without defeat. Almeria are much closer to the danger zone than their victors, 14th in the tablle, but are safe in the knowledge that they will still have a four-point margin over 18th placed Valladolid come next weekend.
Levante wasted no time in reminding the visitors of their physical nature as David Navarro picked up a yellow card with less than two minutes played for an elbow on Jonathan Zongo.
Zongo had an opportunity to get revenge immediately when he rose to meet a cross from Aleix Vidal, but the Burkina Faso international headed high over the bar.
Levante could have taken the lead in the first half had they made more a mistake by Almeria's Rafita, whose misplaced pass found Levante forward Nabil El Zhar, who cut the ball back to Barral, but the striker missed the target.
Barral was a handful for Almeria all evening, and passed up several opportunities to score before finally breaking the deadlock, the best of which came towards the end of the first half, when the striker was foiled by Almeria goalkeeper Esteban from inside the six-yard box.
He even had a goal harshly ruled out for offside right on the stroke of half-time.
Almeria midfielder Vidal produced the finest moment of individual skill of the game 15 minutes into the second half, easing past Levante defenders as he raced towards goal from the left wing, but could only hit the side netting when it came to shoot.
But just a moment later, Barral put Levante ahead with a phenomenal finish, swivelling around the penalty spot to meet a cross from El Zhar first time on the volley, leaving Esteban with no chance.
Almeria created two chances to equalise in the remaining minutes.
First Zongo struck a post with a close-range header, the ball eventually plucked away by Navas, and - with just a minute remaining - the goalkeeper came to his side's rescue again, sticking out a hand to tip over a shot from Diaz after Levante had failed to deal with a ball into the box from Suso.
Baba Diawara could have made it 2-0 in injury time but came just a few inches short of sending Pape Diop's pass into the net.