Leganes had a chance to restore parity in the 35th minute through Alexander Szymanovski but Marc Ter Stegen was on hand to make a great save maintain Barcelona's lead into the break.
Barcelona will be short of options in defence for next Sunday's top-of-the-table clash with Valencia after Gerard Pique was suspended for the game by picking up a fifth booking of the season against Leganes.
"We always try to play our best in every game but sometimes it is not possible".
Barca dominated the early possession and thought they had gone ahead in the fourth minute when Luis Suarez fired into the empty net from close range, but an offside flag was up against Jordi Alba in the build-up.
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We will use him for sure, but to bring him in now for 90 minutes is an absolute no. Anyone who knows Adam will know how ready he is.
Having beaten Bilbao and held Atletico to a goalless draw so far at home this season, the trip to Leganes certainly won't be an easy task for Barca as they look to take another step to securing the league title.
"Perhaps 0-3 is a bit excessive".
"I wasn't anxious. The important thing was to feel good again and help the team", added Suarez.
However Gerard Pique will miss next weekend's game against Valencia, as the central defender was given a yellow card for wrapping his arms around Nordin Amrabat, the striker on loan from Watford.
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Suarez was booked for a tangle with Cuellar, though the goalkeeper made the most of minimal contact, and the Barca star gleefully rubbed it in the goalkeeper's face when he scored his second scrappy effort of the game shortly afterwards. "The first half was tight but things opened up in the second".
While Luis Suarez and Paulinho kept the goals flowing at the other end there was no way past the formidable Ter Stegen as he clinched a clean sheet.
In the 90th minute, Messi's brilliant work down the left flank rattled the Leganes defence yet again as his flicked pass found Paulinho who tapped in Barcelona's third which handed Leganes their third straight defeat in the Spanish La Liga Santander this season.
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He soon broke again and he eased to victory as he set up a meeting with Federer . Play was fast and fiery from the opening point with both players on the attack.