Zaragoza ends drought with road win
Midfielder Jose Maria Movilla pounced on a loose ball in the penalty area and, having drawn goalkeeper David Cobeno out, deftly crossed the ball for Zuculini to slot it into the net in the 21st minute.
Zaragoza enjoyed greater possession in the second half.
Helder Postiga headed the ball into the area from a throw-in, and Galdeano unleashed a powerful shot that beat Cobeno in the 60th.
Zaragoza rose one spot above Rayo to 12th in the league standings with both teams on 19 points.
Barcelona is top, six points in front of second-place Atletico Madrid and 11 ahead of defending champion Real Madrid.