A second half header from Raul De Tomas was enough to earn Rayo Vallecano three points at Alaves and see the Madrid side climb out of the bottom three.
It was the visitors who went close early on when Martin Aguirregabiria missed a through pass, allowing Alex Moreno to race onto the loose ball and get a shot away, but it was well kept out by Fernando Pacheco.
At the other end, Mubarak Wakaso’s cross was met by Jonathan Calleri, but his glancing header was well wide. Two minutes later, the forward again met a cross but once more his header was off target, this time over the bar.
Calleri continued to cause problems for the Rayo defence and he had another chance when he controlled a Wakaso cross well before firing a volley over the bar.
The bright start to the game fizzled out, with the rest of the half as damp as the conditions out on the pitch as the rain continued to pour down.
There was one final chance in the final minute of the half though, which fell the way of Burgui, but the Alaves attacker’s shot came crashing back off the post as the sides went in level at the break.
However, it took just two minutes of the second half for the opening goal to come and it went the way of Vallecano.
Oscar Trejo managed to dig out a shot which clipped the post but Luis Advincula was able to quickly return the ball into the middle where Raul De Tomas headed home his ninth La Liga goal of the season.
Just past the hour mark, Alaves went close with Burgui’s shot deflecting wide off Abdoulaye Ba but the Basques were struggling to break Rayo’s resistance.
With twelve minutes remaining, two crosses from Jony caused havoc in the box, his first just evading Calleri with his second being headed wide by Guillermo Maripan.
Calleri had one final chance when he volleyed wide from the edge of the area with substitute Bebe forcing Pacheco into a save deep into stoppage time, as Rayo threatened a second at the other end but one goal was enough to claim the three points.
The win sees Rayo make it four wins and a draw from their last five games to climb out of the relegation zone, with Celta Vigo dropping down alongside Villarreal and Huesca. Alaves remain fifth.
Alaves: Pacheco; Martin, Laguardia, Maripan, Duarte; Burgui (Sobrino, 75), Manu (Jony, 67), Brasanac, Wakaso; Calleri, Baston (Guidetti, 75)
Rayo Vallecano: Dimitrievski; Advincula, Velazquez, Ba, Amat, Moreno; Embarba (Garcia, 66), Comesaña, Imbula, Trejo (Bebe, 80), De Tomas (Medran, 87)