Title-chasing Atletico fell behind inside two minutes against Joaquin Caparros' men, Andreas Ivanschitz giving the visitors the lead with a close-range finish.
Atletico looked to have turned things around as a Diego Godin header and a smart finish from Diego Costa put them in front, only for Levante midfielder Pedro Rios to equalise on 56 minutes with a fine solo goal.
Costa proved to be the difference, though, the striker scoring his 23rd goal of the season from the penalty spot following Ruben Garcia's foul on Juanfran, whose Levante namesake was sent-off in injury time.
Victory puts Atletico three points clear at the top of La Liga, although defending champions Barca will reassume the position at the summit if they beat Getafe by more than one goal on Sunday.
Villarreal's UEFA Champions League hopes were dented by a 2-1 home defeat to 10-man Sevilla.
Defender Juan Cala put Sevilla in front with a 24th-minute header and striker Carlos Bacca added a second as he capitalised on Mateo Musacchio's failed clearance midway through the second half.
Goalscorer Cala was dismissed four minutes from time for his challenge on Jaume Costa before Jeremy Perbet gave Villarreal hope with a late penalty.
Real Sociedad leapfrogged Villarreal into fifth with a 3-1 success at Granada, a Carlos Vela double and Antoine Griezmann's 14th strike of the season making sure of the points for the Basque outfit.
Elsewhere, Almeria ended a three-game winless streak in the league as Ramon Azeez's fourth-minute goal gave them a 1-0 victory at Real Betis.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.