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.
Atletico are now level with Barcelona in second place and one point behind leaders Real Madrid, with the latter two sides in action against Real Sociedad and Valencia respectively on Sunday.
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.
"More than just the goals, which are important for him and the team, I like when he tracks back, works and when he wins the ball back to be able to attack from better positions," Simeone said of Griezmann.
"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.
Atletico looked to have made the game safe just 60 seconds into the second period as, despite more heroics from Marino to claw a Mandzukic header off the line, he couldn't react in time to prevent Griezmann's follow-up effort crossing the line.
However, the hosts were pegged back just after the hour mark when Levante halved the deficit.
Mandzukic was again heavily involved as he did brilliantly to turn Victor Casadesus's header off his own line, but the ball fell to Ivan Lopez and his drive clipped El Zhar on its way into the far corner.
Simeone then withdrew Turan and Mandzukic with one eye to Wednesday's repeat of last seasons' Champions League final against Real.
And, not for the first time this season, the Argentine's side needed to rely on their threat from set-pieces to seal the three points eight minutes from time when Godin headed home Tiago's in-swinging cross.
Elsewhere, Sevilla moved above Valencia into fourth, but were far from convincing in a 1-0 win over 10-man Celta Vigo.
The visitors were forced to play 70 minutes with a man less after Carles Planas was shown a straight red card for chopping down Denis Suarez.
Nico Pareja then scored the only goal of the game from a free-kick 12 minutes later to continue Sevilla's unbeaten record at home this season.
Villarreal lost ground in the fight for the Champions League places as they let a two goal lead slip away to bottom side Elche to end a seven-game winning streak in a 2-2 draw.
Malaga are now three points off the top four after a controversial Tomer Hemed late penalty handed Almeria a 2-1 win at La Rosaleda, whilst Deportivo la Coruna moved out of the relegation zone thanks to a 1-0 victory over Athletic Bilbao.