With Fernando Torres watching on from the stands before his move back to his boyhood club is concluded on Monday, Griezmann was under pressure to continue his fine form after scoring a hat-trick as Atletico closed 2014 with a 4-1 win away to Athletic Bilbao two weeks ago.
And he duly obliged with two headed finishes from close range early in each half before Diego Godin nodded in Atletico's third after Nabil El Zhar's deflected effort had given Levante hope yesterday.
Torres was the star attraction before kick-off as he took his seat in the directors' box to much acclaim.
However, on the field, Griezmann ensured Los Rojiblancos' former captain will find it hard to get into the side for the visit of Real Madrid in the Copa del Rey on Wednesday.
Atletico coach Diego Simeone, though, suggested Griezmann could eventually move out wide, where he has played for the majority of his career, to make way for Torres.
"He can play in different positions, as well as on the wing where he has played before. Not all games are equal and there could be times when all the forwards play."
Griezmann put Simeone's men in front on 18 minutes when Guilherme Siqueira's cross from the left looped into the Frenchman's path and he nodded past the helpless Diego Marino.
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