The sides came into the game at Estadio Ciudad de Valencia locked on 19 points in the relegation zone, but it was Lucas Alcaraz's side who edged a game featuring three goals and three red cards.
Youssef El-Arabi put Granada into a 13th-minute lead from the penalty spot, though the game came to life 18 minutes from time when Adrian Colunga was sent off for a cynical trip on Barral.
Ivan Ramis and El-Arabi were given their marching orders seven minutes later for an off-the ball clash, leaving Abel Resino's visitors short of options.
And it proved to be their undoing as Victor Camarasa capitalised on Oier Olazabal's weak punch to volley home from the edge of the area.
Levante poured forward and had their reward in the fourth minute of stoppage time, Barral latching onto Kalu Uche's flick amid offside claims from Granada to curl beyond Olazabal and seal a vital three points.
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