The striker, on loan from Real Madrid, nodded home his ninth league goal of the season from close range to earn Rayo their fourth win from five matches.
Rayo's surge in form has helped them rise to 17th place, two points clear of Galician side Celta Vigo.
Fifth-placed Alaves were far below their best and fell to their first defeat at Mendizorroza all season, with Abelardo's side winning just two of their last nine in all competitions.
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(Reporting by Rik Sharma; Editing by Ken Ferris)
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