France international Griezmann hammered home a second-half penalty after a handball by Nikola Vukcevic for his ninth league goal of the season, sending Atletico two points behind League leaders Barca, who host Eibar later on Sunday.
Levante defeated a much-changed Barca in the Copa del Rey in midweek, but they posed minimal threat to Diego Simeone’s side at the Wanda Metropolitano, only really testing Jan Oblak once throughout the match.
It was far from a vintage performance from Atletico, who have now won their last two home La Liga matches 1-0 courtesy of a Griezmann penalty
Griezmann was unable to convert a glorious chance from inside the six-yard box before Atletico lost Stefan Savic to a left thigh injury sustained off the ball in the seventh minute.
The hosts thought they were in front when Koke slotted home Vitolo’s pass four minutes later but it was ruled out after referee Eduardo Prieto Iglesias reviewed footage of Rodrigo’s challenge on Enis Bardhi in the build-up.
An excellent tackle from Rober Pier stopped Vitolo firing Angel Correa’s great throughball home before half-time, while Koke and Thomas Partey kept the pressure on after the restart.
Atletico got the leap forward in the 57th minute when Vukcevic obstructed Thomas’ cutback with his arm and Griezmann fired the resultant penalty into the top-right corner.
Oblak stayed caution to deny Jose Luis Morales after he cut in from the left, before Bardhi was blocked by Diego Godin inside the last 10 minutes as Atletico made it 16 La Liga matches without defeat.