But for a brilliant second-half save from Jan Oblak to deny Nabil El Zhar, Leganes could even have registered their first ever win over Atletico in the top flight.
A third draw in seven games this season sees Atletico fall a point behind Sevilla, who moved up to second earlier with a 2-0 win over Malaga.
Barca can extend their lead at the top to five points with victory at home to Las Palmas tonight.
Atletico boss Diego Simeone made four changes from the team that started against Chelsea in an attempt to refresh his side.
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However, the visitors still looked leaden-footed and confused by a change of system to three at the back.
And Simeone blamed his side's effort against the English champions as well as a demanding early season schedule that has seen Atletico play just three of their nine games so far this season at their new Wanda Metropolitano stadium.
"The boys have played a lot of games in quick succession since the last international break," said Simeone.
"Given the difficulties of all the away games we've had, the Champions League games and having to get used to our new home, I think we are in good shape."
El Zhar was introduced at the break and quickly stung the palms of Oblak.
However, it took a sensational one-handed stop from the Slovenian on the hour mark to turn El Zhar's next effort over for a corner.
Despite Atletico's lack of cutting edge in the final third, Simeone took the strange decision to replace top scorer Antoine Griezmann with full-back Sime Vrsaljko 25 minutes from time.
"The rest of the strikers and the team have to help him to play closer to the area and create more chances so it doesn't solely fall on him."
However, without the Frenchman the best Atletico could muster was a Diego Godin header that Cuellar comfortably turned behind.
A point continues Leganes' fine start to the season as they move level with Real Madrid on 11 points in sixth.
By contrast, a sixth defeat in seven games pushes Malaga boss and legendary former Real Madrid player Michel ever closer to becoming already the fourth managerial change of the La Liga season.
Ever Banega coolly dispatched the spot-kick and just two minutes later Luis Muriel showed great pace to burst clear from the halfway line into the Malaga box before firing inside Roberto's near post.
Alaves ended a run of six defeats to start the season with a 2-0 win at Levante thanks to goals from Munir El Haddadi and Alvaro Medran.
Amath Ndiaye put the visitors in front at La Riazor, but Lucas Perez levelled with his first goal since returning to the club on loan from Arsenal before Florin Andone grabbed the winner three minutes from time.