Apono hit a brace and Rodri was also on target as Zaragoza hauled themselves out of the relegation zone at the expense of Deportivo La Coruna.
Zaragoza ended a 15-match winless streak in the league with a dramatic 3-2 win over Real Mallorca last time out, and the momentum of that victory was much in evidence on Sunday as they comprehensively outplayed their top-10 ranked visitors.
The hosts left it late to see off Mallorca and were in no mood to put their fans through the mill again on Sunday, instead taking the match to their visitors.
Paco Montanes had their first chance in the fourth minute with a shot that whistled by the post, while a short time later Alvaro's close-range header from Apono's free-kick was kept out by Ruben.
The hosts' early pressure told after 25 minutes when Abraham's shot was harshly adjudged to have struck the hand of Jordi in the area and the referee pointed to the spot.
Apono took the responsibility from 12 yards and sent the goalkeeper the wrong way.
Rayo threatened just once in the half, Alejandro Dominguez's 25-yarder drawing a good save from Roberto.
The hosts needed only six minutes of the second period to extend their lead, Rodri snaffling up the rebound from close range after Helder Postiga had seen his header parried by Ruben.
Dominguez remained Rayo's only outlet in the final third and he provided a rare moment of threat with 17 minutes left when his shot from six yards was saved by Roberto.
Postiga was denied a goal when his header struck the post in the first minute of added time, but a third did arrive with seconds remaining when Apono fired in from 20 yards as Zaragoza claimed consecutive wins in La Liga for the first time in 12 months.