Barcelona extended their impressive unbeaten run this season in the Spanish LaLiga to 12 games after defeating Leganes 3-0 at the Butarque Stadium on Saturday.
Suarez was refreshed after sitting out worldwide duty with Uruguay over the past fortnight and had the ball in the net after just four minutes, but Jordi Alba had already been flagged for offside as he supplied the cross for the former Liverpool striker.
The Catalans started the match with the same line-up that dispatched Sevilla before the worldwide break with Suarez and Lionel Messi continuing to lead the line.
Barcelona haven't lost in the league all season and have won 10 of their 11 games.
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.
Three minutes later Paco Alcacer picked out Suarez with a cross from the right, but the Uruguayan's acrobatic effort was blocked by Dimitrios Siovas.
Alcacer was again heavily involved as his close-range effort from the left of the area was pushed clear by Cuellar, but the ball fell to Suarez whose half-volley went into the net off the foot of Ruben Perez.
Leganes responded as Amrabat turned past Gerard Pique only to find Ter Stegen storming off his line to smother his shot.
However, Barca piled more pressure on the chasing Atletico and Real ahead of the Madrid derby and rubbed salt into Leganes´ wounds when Paulinho rolled into an empty net when a loose ball broke off Messi in stoppage time.
The only sour note for Barcelona - who travel to Juventus in the Champions League on Wednesday - was a first-half booking for Pique which means he will now miss their league trip to Valencia next weekend.
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