The Rojiblancos fell behind in the 78th minute but Alvarez, who had opened the scoring, struck twice more in the final stages to claim three points for Diego Simeone's side.

The Argentina international helped Atletico secure only their second win from six league matches during a shaky start to the campaign.

Atletico are ninth and trail league leaders Real Madrid by nine points ahead of Saturday's derby clash against Xabi Alonso's side.

"We needed to get three points to get confidence from winning, we've been playing well but because of small details we weren't getting good results," Alvarez told Movistar.

"We have to keep working and improve some things to get on a winning run."

Alvarez, who missed a penalty in Atletico's frustrating draw at Mallorca last weekend, opened the scoring at the Metropolitano stadium.

The 25-year-old, who joined from Manchester City in 2024, volleyed home from Marcos Llorente's looping cross after 15 minutes to get the ball rolling.

The striker should have netted a second before half-time but fired high over the crossbar from Nahuel Molina's perfectly-judged ball.

Visitors Rayo made the hosts pay in first-half stoppage time when Pep Chavarria scored one of the goals of the season, a bullet from distance which ripped into the top corner past Atletico goalkeeper Jan Oblak.

Rayo substitute Alvaro Garcia sent his team ahead when played in on goal, rounding Oblak before squeezing home from a tight angle.

It enraged Atletico and they began pouring forwards, quickly finding an equaliser.

Rayo goalkeeper Augusto Batalla kept out an effort from Simeone's son Giuliano, but Alvarez was on hand to blast the rebound home from point-blank range.

Giuliano crashed a shot off the crossbar as Atletico pushed for a winner.

With Rayo rocking Alvarez completed his treble in the 88th minute, producing a superb finish to beat Batalla from the edge of the box.

After grumbling about being substituted during the Mallorca game, Alvarez showed his coach against Rayo why he is best left on the pitch.