The 4-0 win at Wanda Metropolitano Stadium moved Atletico within four points of the Catalan club, which plays at Las Palmas on Thursday.
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Atletico’s next league game is against Barcelona at Camp Nou Stadium.
Diego Simeone’s team has won eight straight matches in all competitions, including six in a row in the league.
Griezmann has 12 goals in his last nine matches. He reached 15 goals in La Liga, surpassing Cristiano Ronaldo for fourth in the scoring charts behind Iago Aspas, Luis Suarez and Lionel Messi.
His three goals against Sevilla came in a 5-2 league win on Sunday.
”I’m happy with my performance,” Griezmann said. ”The most important thing was to earn the three points, and now we go to Barcelona to see if we can do something good there.”
He opened the scoring from inside the area after a long low pass by Koke in the 26th, then added to the lead less than 10 minutes later with a well-struck free kick. His third goal came from inside the area after a cross by Filipe Luis early in the second half, and the fourth was a 67th-minute header after being set up by Diego Costa.
Griezmann had already struck the crossbar with another free kick in the first half, and later missed from inside the area in a one-on-one situation with goalkeeper Ivan Cuellar.
Costa also came close to scoring while one-on-one with Cuellar midway through the second half, and Diego Godin had a goal disallowed for offside a few moments later.
Leganes, 14th in standings, also struck the crossbar in the first half. The southern Madrid team hasn’t won in eight matches in all competitions, including six in a row in the league.
There was a minute of silence before matches to honor former Barcelona and Sporting Gijon striker Enrique Castro ”Quini,” who died of a heart attack on Tuesday. He was 68.
It just keeps getting worse for Clarence Seedorf with Deportivo La Coruna, which lost 3-0 at Getafe to remain winless and scoreless since the former Dutch midfielder took over as coach four rounds ago.
Deportivo hasn’t won in 11 straight matches and is second-to-last in the standings, in the relegation zone.
It lost its first two matches under Seedorf and drew the third one, all without scoring. This is Seedorf’s third attempt at coaching after brief stints with AC Milan in 2014 and a Chinese club in 2016.
”We have to keep working hard,” Seedorf said. ”In three days we have another match.”
Getafe, which has lost only one of its last eight games and is eighth in the standings, got on the board with Angel Rodriguez, Jorge Molina and an own goal by Deportivo defender Eneko Boveda.
Valencia was held to a 1-1 draw by Athletic Bilbao, missing a chance to overtake Real Madrid for third place.
Geoffrey Kondogbia put Valencia ahead midway through the first half, but Oscar De Marcos equalized for the hosts shortly after halftime at San Mames Stadium in Bilbao.
Athletic missed a penalty kick with Valencia leading 1-0, as Aritz Aduriz’s shot was stopped by goalkeeper Neto.
The result left Valencia one point behind Madrid, which on Tuesday lost 1-0 at Espanyol without Cristiano Ronaldo and other regular starters.
Sevilla rebounded from a humiliating 5-2 loss at home to Atletico Madrid by defeating last-place Malaga 1-0 with an early goal by forward Joaquin Correa at La Rosaleda Stadium.
The victory moved Sevilla within eight points of fourth-place Valencia, which is currently holding the last Champions League spot.
Malaga has lost five in a row and hasn’t won in 11 consecutive matches, losing nine times during that streak. It has 13 points from 26 matches, five points less than second-to-last-place Deportivo La Coruna.