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With Valencia not scheduled to play until Monday, Sevilla found themselves with the opportunity to move above them into the last Champions League place - a chance that they looked determined to seize from early on.
The hosts fashioned a number of promising early openings but failed to convert, with Benoit Tremoulinas venturing forward from defence before firing wide, while Denis Suarez vaguely tested Antonio Tono.
It was a sign of things to come, as Iborra opened the scoring on 17 minutes, chipping the ball home from 10 yards out following good work from Diogo Figueiras.
Rayo would have been two down shortly before the half-hour mark if not for Tono, whose excellent instinctive save kept out Kevin Gameiro from a matter of yards. Tono replicated those heroics to deny Gameiro again before the break, but Carrico succeeded where he failed by heading home from the slimmest of angles on the stroke of half time.
Paco's Vallecano charges started the second half much better and thought they had reduced the arrears on 51 minutes, but Grzegorz Krychowiak's own goal was ruled out after Manucho was adjudged to have been offside in the build-up.
Unperturbed, the visitors carried on in the same vein as Javier Aquino dragged his effort narrowly wide on the hour mark in a opportunity that woke the hosts up once again. Tono was again tested on 73 minutes when Jose Antonio Reyes embarked on a lengthy run from his own half, but his final effort on the edge of the box was tipped past the post.
Roberto Trashorras and Alejandro Pozuelo both spurned late chances to keep their hopes of a comeback alive, but in the end Rayo paid the penalty for wayward finishing as Sevilla leapfrog Los Che for 24 hours at least.