- Leganes 1-5 Barcelona
- Goals from MSN secure win
- Rafinha nets fifth goal
- Barcelona goes level with Real Madrid
First-half goals from MSN -- the first time the trio have scored in the opening 45 minutes away from home -- set the tempo, before the result was sealed after the break thanks to Messi's second and a Rafinha bullet.
Leganes did get a consolation, as Gabriel bent a superb free-kick around the wall and out of the reach of Marc-Andre ter Stegen.
It means Barcelona has now scored 12 goals in five days, after its 7-0 demolition of Celtic in the Champions League.
"We made use of the space and we were switched on from the start," manager Luis Enrique said after the match.
"The tactical set up did have its risks but we faced up to it well and I am proud."
Barcelona was looking to avoid a second consecutive defeat to a promoted club, after a shock 2-1 defeat against Alaves at the Nou Camp last weekend and Messi settled any nerves inside 15 minutes.
Suarez clumsily bundled his way down the right, before passing the ball square to Messi for the Argentine to turn in at the near post.
It was the first La Liga goal ever scored at Leganes' Municipal de Butarque stadium and Messi's 34th at a different ground, surpassing Real Madrid legend Raul's previous tally of 33.
Up until the opening goal, Leganes had more than held its own against the reigning La Liga champion, but the Barcelona front three find scoring easy enough without chances being presented to them on a plate.