With new loan signing Fernando Torres watching from the stands, the in-form Frenchman nodded in a deflected Guilherme Siqueira cross after 18 minutes against a Levante side that struggled to cope with the physicality of the hosts.
Griezmann, who grabbed a hat-trick in Atletico's final game before Christmas against Athletic Bilbao, then notched his eighth league goal of the season in the 47th minute as he headed in after Mario Mandzukic's effort was saved by Diego Marino.
Substitute Nabil El Zhar deflected an Ivan Lopez shot into the net for sixth-from-bottom Levante before Diego Godin sealed the win with eight minutes to go thanks to another header.
"We should have finished off the game in the first half but we did not pressurise enough," Godin told reporters. "My goal calmed us down as we had become nervous after conceding.
"It was important for us to finish the year winning and also start with another victory."
Atletico are third and level on 38 points with Barcelona, who face Real Sociedad on Sunday when leaders Real Madrid, a point clear, take on Valencia looking to extend their 22-match winning streak.
Elsewhere on Saturday, a Nico Pareja free kick gave Sevilla a 1-0 victory over 10-man Celta Vigo that moved them up to fourth with 33 points.
Celta started well but were dealt a heavy blow when Carles Planas was harshly dismissed for bringing down Denis Suarez after 22 minutes.
Ten minutes later Hugo Mallo upended Vitolo 25 metres out and Pareja blasted the ball home with keeper Sergio Alvarez slow to react.
Eighth-placed Celta, who have lost six league games in a row, looked dangerous on the break but lacked a cutting edge and have now gone seven matches without a goal.
Villarreal’s five match winning run in La Liga came to an end as bottom side Elche came from behind to draw 2-2.
Luciano Vietto and Ikechukwu Uche put sixth-placed Villarreal into a commanding lead but Jonathas and Victor Rodriguez brought the home side back on level terms still before half time.
Malaga were beaten 2-1 at home by Almeria and Deportivo La Coruna won 1-0 against Athletic Bilbao.
(Editing by Tony Jimenez/Peter Rutherford)
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