The visitors had started brightly but Helder Postiga fired wastefully over after just two minutes before heading an even better chance from close range over 15 minutes later.
However, Mallorca's set-pieces troubled Zaragoza all day and Victor headed in unchallenged from Chori Castro's corner just after the half-hour.
Manolo Jimenez's men had more of the ball after the break but could not find a way through a well-organised Mallorca back line. They remained five points from safety with only four games remaining.
The win ensures Mallorca will definitely play top-flight football for the 16th consecutive season and they probably just about deserved the three points from a match in which neither side shone.
Zaragoza's best openings came early on as Postiga blazed over when presented with a good shooting opportunity on the edge of the area after just two minutes and the Portugal forward should have put his side in front as Luis Garcia's curling free-kick found him free at the back post but he headed wide.
Mallorca then began to take control of the game and Jose Manuel Chico was unfortunate not to give them the lead as he swept home a corner from the left but was wrongly flagged offside.
Moments later, though, the hosts were in front as this time Castro's ball in from the right found Victor and he powered his header past Roberto to record his eighth goal of the season.
The roles were reversed just after the break as this time it was Castro who got on the end of Victor's free-kick but the Uruguayan just could not keep his effort on target.
Zaragoza kept probing and trying to work opportunities throughout the second half but the closest they came to an equaliser was another Postiga shot that rattled into the side-netting with eight minutes remaining.