Andreas Ivanschitz had stunned the Vicente Calderon inside two minutes as he slotted home the first league goal Atletico had conceded at home since early October.

However, Atletico gradually took control of the game and were deservedly level when Diego Godin headed home Juanfran's cross on the half hour mark.

Costa then put the hosts in front two minutes after the break, but Levante responded as a wonderful individual effort from Pedro Rios brought them level 10 minutes later.

Atletico weren't to be denied, though, and when Ruben Garcia clipped Juanfran inside the area 13 minutes from time, Costa's spot-kick just had enough power to beat Keylor Navas.

Barcelona can restore top spot if they beat Getafe away on Sunday, whilst Real Madrid can also cut the eight-point gap between them and their city rivals when they travel to Valencia.

"The best thing about the game was the result," said Atletico boss Diego Simeone.

"We had to try different styles of play and we kept going from the second minute until the 93rd."

Top spot represents a remarkable turnaround at the club since Simeone took charge just short of two years ago.

However, he insisted they won't get ahead of themselves as they challenge for trophies on three fronts come 2014.

"We have got this club moving towards one goal and were not going to compromise on our philosophy of treating every game like it's our last.

"I will never tire of saying it. We are aware of our limitations and the difficulties we face.

"We have to keep working every day and rowing in the same direction to reach our goal."

Before kick-off on Saturday the talk was of Atletico racking up the score to ensure top spot at Christmas for the first time since 1996.

But they were rocked by the first attack of the game when Nikos Karabelas played in Ivanschitz to slot across goalkeeper Thibaut Courtois into the far corner.

Courtois then had to produce a stunning save from David Barral to prevent Levante making it 2-0.

However, Atletico finally settled and were level when Juanfran's in-swinging cross was met powerfully by Godin.

Costa then got the goal which moved him ahead of Cristiano Ronaldo as La Liga's top scorer just two minutes after half-time with a sensational volley at the back post from Gabi's free-kick.

The lead lasted only 10 minutes as the hosts were caught out from their own corner and Rios galloped clear on the counter-attack before drilling low past Courtois from the edge of the area.

Atletico then poured forward in search of a winner and were rewarded when Juanfran enticed a naive challenge from Garcia and Costa rolled home his 19th league goal of the season.

Levante's frustration was encapsulated as their captain Juanfran saw a red card in stoppage time for lashing out at Filipe Luis.

Earlier, Sevilla enhanced their chances of Champions League football next season with a 2-1 win away to Villarreal.

Goals from Cala and Carlos Bacca put the visitors on course for the three points before Jeremy Perbet pulled a late goal back from the penalty spot.

Real Betis remain rooted to the foot of the table after they lost 1-0 at home to fellow strugglers Almeria.