The Frenchman scored twice, his 10th and 11th goals of the campaign, to give Diego Simeone's side the perfect start to 2015
Griezmann broke the deadlock in the 18th minute with a towering header from Guilherme Siqueira's cross and doubled the tally shortly after the restart by just nodding over the line after Diego Marino kept out Mario Mandzukic's initial effort.Nabir El Zhar gave the home side a fright when he pulled a goal back with 62 minutes on the clock, but Diego Godin's header with eight minutes of normal time remaining secured Atletico all three points.
Atleti's victory adds to the feel-good factor at the Calderon born out of the announcement earlier this week that Fernando Torres, who took a watching brief from the stands, is to re-join the club.
Diego Simeone's side move level on points with second-placed Barcelona and are now just one point adrift of leaders and city rivals Real Madrid, although Carlo Ancelotti's side have two games in hand.
Atleti enjoyed a near monopoly of possession in the opening stages and Arda Turan had a goal ruled out in the 12th minute as Godin - who nodded the ball into his path - was offside.
Mandzukic was next to go close as he headed Siqueira's cross from the left wide when off balance.
The breakthrough came in the 18th minute when another fine Siqueira delivery picked out Griezmann, who planted a firm header past a helpless Diego Marino at the near post.
Atleti continued to turn the screw and Turan flashed an effort just over from 25 yards before Mandzukic also had a goal chalked off at the near post for what appeared to be offside, although replays also showed the Croatian had handled the ball.
Levante then had Diego Marino to thank for keeping the score at 1-0 when he produced a superb point-blank stop from his own defender Loukas Vyntra, who diverted Koke's cross goalwards.
Diego Marino was desperately unlucky to be beaten for the second goal in the 47th minute. The goalkeeper made a smart stop from Mandzukic's header before leaping back across goal to get a hand to Griezmann's follow-up, but the ball was just over the line.
More good work from Mandzukic and Griezmann led to Tiago almost adding a third with a curling effort that was deflected wide.
Levante, who had offered little going forward, found a way back into the game in the 62nd minute.
The hosts scrambled a corner to safety, but their defence was left static when Victor Casadesus drilled the ball back into the area and El Zhar - who had been on the pitch for just two minutes - got the final touch past Miguel Angel Moya.
However, Godin put the game beyond doubt in the 82nd minute with a looped header from Tiago's cross from the left flank as Atleti started the new year with a comfortable win.