Almeria came into the clash without a victory in six previous outings and, despite having the better of the play, they were unable to break down their stubborn opponents.
Just when it looked like both sides would have to settle for a point, Kakuta - on loan from Premier League side Chelsea - struck from close range to steal all three points for the visitors.
The win - Vallecano's second in succession - lifts them a couple of places in the table to 10th, while Almeria remain mired in trouble, just one position above the relegation zone.
Following a goalless first half, Almeria's Thievy Bifouma went agonisingly close to an opener in the 52nd minute, fizzing a low left-footed shot narrowly wide of the far post with goalkeeper Cristian Alvarez well beaten.
The home side continued to press forward with great urgency, but they were just unable to carve out a clear goalscoring opportunity.
Then, with four minutes remaining, Kakuta met Alberto Bueno's teasing cross on the volley with a controlled finish into the roof of the net to secure maximum points for his side.