After Luis Enrique's men suffered a shock 2-1 loss to Alaves last round, their attacking trio, who started together for only the second time this season, combined for a goal apiece to establish a 3-0 lead.
It was the first time Messi, Suarez and Neymar have scored at least one goal each in a La Liga game before the end of the first half.
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Messi opened the scoring in the 15th minute courtesy of a Suarez cross while Leganes found themselves 2-0 behind when Unai Lopez rolled a pass into the Argentinian's path, allowing him to return the favour to the Uruguayan as je rolled the ball into an unguarded net.
Neymar's enjoyed his own tap-in courtesy of a Suarez assist in the 54th minute followed by a Messi spot-kick high into the right corner of the net to bag his second.
Rafinha got in on the scoring action, cutting inside to pick out the top corner left-footed from 20 metres out.
Gabriel's ensured a Leganes consolation goal in the 80th minute with a free-kick but the game belonged to Barcelona and their attacking trio who have scored 68 per cent of the total goals netted by Barcelona across all competitions this season.
