The Brazil-born striker took his tally for the season to 19 goals with a left-footed volley and a game-deciding penalty, as Diego Simeone's men eked out a vital win
Andres Ivanschitz put the visitors ahead after just a minute of action but the Rojiblancos leveled matters through Diego Godin on the half-hour mark.
Diego Costa then volleyed Atletico into the lead early in the second half and although Pedro Rios restored parity, the Brazil-born forward took his Liga tally for the season to 19 goals with a penalty.
The Rojiblancos had gone into the game level on points and goal difference with Barcelona, meaning that by bettering the Catalans' result against Getafe on Sunday, they would reach the winter break on top of the table. Consequently, the target was another resounding victory.
However, an expectant Vicente Calderon was silenced with less than 60 seconds of the game elapsed, with Ivanschitz slotting home after making a wonderfully-timed run into the area and then taking a through-ball in his stride.
Atletico slowly but surely began to take control of the game, and it equalized when center half Godin rose at the near post to head home a floated cross from Juanfran right on the half-hour mark.
The hosts could have taken the lead five minutes later but Keilor Navas did wonderfully well to get to save at the feet of Diego Costa.
Levante then lost Ivanschitz to injury as Atletico continued to pour forward, with David Villa going close with a deflected effort.
The Rojiblancos were unable to find a way through before the break, though, and could even have conceded right on the stroke of halftime, but Barral fired wide after beating Courtois to a through-ball.
It proved a costly miss because Atletico moved in front just over a minute after the restart, with Diego Costa appearing at the back post to beat Navas with a low, left-footed volley from Gabi's deep free kick.
Atletico seemed poised to coast to a comfortable win at that point but Rios levelled matters in sensational style in the 56th minute, pouncing on a mistake by Koke before driving past Filipe Luis and then unleashing an unstoppable 20-yard drive past Courtois.
The home side pressed for a winner and found one when Ruben Garcia clumsily felled Juanfran in the area, thus allowing Diego Costa to decide an enthralling encounter in Atletico's favor with a penalty that Navas will feel he should have saved.
Levante's frustration at being denied a deserved point spilled over in the dying seconds when Juanfran, who had been struck by Tiago during an off-the-ball incident in the first half, was sent off for lashing out at Filipe Luis.
Diego Costa then missed a great chance to complete his hat trick but there was no taking the shine off a win that will send Atletico into the winter break at the very least level on points with reigning champion Barca.