Paulo Da Silva's handball gave Rayo the perfect opportunity to make a winning start at home on their return to La Liga but Roberto Jimenez saved Fuego's penalty with 20 minutes remaining.
Zaragoza offered little as an attacking threat and Angel Lafita's tame effort in the first-half was their best effort on goal.
Buoyed on by a vociferous home crowd Rayo started brightly and Roberto had to turn away a fierce shot from Piti on 11 minutes.
Moments later the home side came close again when 37-year-old Jose Movilla, who scored Rayo's equaliser against Athletic Bilbao two weeks ago, nearly repeated the feat but saw his header clip the top of the bar.
Dani Gimenez was called into action for the first time on 20 minutes to save Lafita's shot from 20 yards but the home side were soon on the attack again and had claims for a penalty waved away when Zaragoza right-back Efrain Juarez collided with Miguel Perez.
The game became extremely scrappy either side of half-time with neither side threatening to break the deadlock until Da Silva's handball left Alvarez Izquierdo with no doubt in pointing to the spot this time.
Fuego stepped up and hit the ball firmly to Roberto's right but the former Benfica keeper guessed correctly and made a superb save.
Both sides had half chances to win it as Raul Tamudo and Juan Carlos shot over before Roberto was forced into one final save from a Andrija Delibasic header.