Atletico Madrid pulled level on points with the Catalans with a 1-0 victory of their own against Getafe earlier on, their 11th straight win across all competitions.
Leganes defender Sergio Gonzalez headed home from a corner after four minutes for the visiting minnows and Barcelona missed a host of presentable chances as they failed to mount a comeback.
After a superb start to the season, Barcelona have lost three of their last six league games and won just one of those, seeing their lead whittled away.
Hansi Flick's side lead third-place Real Madrid by a single point, after the champions drew at Rayo Vallecano on Saturday, having played one extra game than both their closest title rivals.
"It was a messed-up game, it's impossible to be happy. I think we started the game half asleep," Pedri told DAZN.
"We woke up, we created chances but we didn't have the spark we needed to get the goal...
"We have to be better in front of goal if we want to win points, we're in a bad run in the league and we have to turn it around."
Barcelona started in the worst possible way as their former youth player Munir El Haddadi broke in down the right and forced a fine save from Inaki Pena at his near post.
From the resulting corner Leganes took the lead, with Sergio Gonzalez powering a header home to stun the Olympic stadium into silence.
From there Barcelona dominated against the visitors, 15th, and created several chances but found an inspired Marko Dmitrovic in their way.
The Serbian goalkeeper twice denied La Liga's top goalscorer Robert Lewandowski in the first half and produced a stunning save to thwart Raphinha, tipping his powerful effort against the crossbar.
Barcelona's teenage wing wizard Lamine Yamal hurt his ankle in a challenge in the first half but despite the pain, continued to play and was his team's most potent threat as usual.
Neither Lewandowski nor Dani Olmo were on song and Barca replaced the pair with Torres and Fermin Lopez for the final 25 minutes, but Leganes held firm.
Raphinha whipped a stoppage time free-kick over the crossbar to end a thoroughly frustrating night as Leganes earned a first away win at Barca.
Barcelona host Atletico in their final match of the year next weekend.
Atletico hot streak
Diego Simeone's Atletico have been in fine form and continued their winning run across all competitions with a deserved home triumph thanks to Alexander Sorloth's goal.
The Norwegian target man came off the bench to head home the winner in the second half for his seventh league goal this season.
"I'll repeat it, I'm boring, I won't change -- until the last day, we'll go game by game," Simeone told reporters when asked if his team could challenge for the title.
"I always say the best result is 1-0 because you work hard in defence and you're effective in attack, if you win 4-3 there are things you have to improve."
Atletico Madrid controlled the first half but could not put away the chances they created.
Two of the most inviting fell to winger Samuel Lino, but he failed to convert on both occasions.
After 69 minutes substitute Sorloth peeled off his marker at the far post and placed a header back across goal and into the net from Nahuel Molina's cross.
Molina was another reinforcement brought on by Simeone, with Atletico's impressive squad depth telling.
"Before the game I spoke with the players about thanking and recognising those who weren't going to start the game," said Simeone.
"There are very important players who are competing in an extraordinary way... it's our biggest strength."
