Atletico have 12 points from five games, having only dropped points against Barcelona who have a 100 percent record from four games and visit Celta Vigo on Wednesday when Real Madrid, with 10 points from four matches, visit Athletic Bilbao.
Atletico controlled the game but they eased off for long spells against a side incapable of putting them under sustained pressure.
Griezmann netted after four minutes with a volley from six metres and wrapped up the win with another close-range finish from a Jackson Martinez pass in the final minute.
“We scored quickly and we were well placed but we stopped looking to build play,” Atletico coach Diego Simeone told a news conference. “We then improved again in the final stages of the game. In the middle section we looked to close the game down too much.”
Valencia’s dismal start to the season continued as they lost 1-0 at Espanyol, with Victor Alvarez scoring in the first half. They are eighth with six points after one win and three draws.
Low on confidence they did not take advantage of early openings for Zakaria Bakkali and Rodrigo Moreno before Alvarez tucked home a Marco Asensio cross after 18 minutes.
There was little rhythm to their game and in the secondhalf they relied on keeper Jaume Domenech to make important blocks to deny Hernan Perez and Asensio. “I have no doubts over my work nor that of the players,” Valencia coach Nuno Espirito Santo told reporters.
“In the first half we were the better side and looked dangerous but then in the second half we didn’t play well.”
Simeone continued with his rotation policy and it was a lively start from Atletico characterised by good link-up play. Gabi Fernandez put the ball back into the box following a corner and Griezmann turned to finished clinically.
Atletico recruited well ahead of the season and the skills of Yannick Ferreira-Carrasco and Oliver Torres meant that they did not miss the injured Koke as they pressed Getafe back.
But Atletico started to relax at the back before halftimeand Stefan Savic hit a firm drive that was just too close to keeper Jan Oblak who made the save.
After the break a mistake by Guilherme Siqueira put Pedro Leon through on goal but he missed the target before Griezmann put gloss on the scoreline for Atletico by slipping the ball home following a well worked move.
Elsewhere, Imanol Agirretxe's hat-trick gave Real Sociedad a 3-0 win at Granada, their first victory of the season which put them on five points from five games.
(Editing by Ed Osmonbd)
