Nordin Amrabat caused the visitors all kinds of problems in the first half, and it was through the former Watford man that they created the game's first meaningful effort in the 20th minute, the striker swerving between Gerard Pique and Ivan Rakitic before firing wide of the far post.
After struggling for possession in the opening stages, Leganes grew into the game and looked dangerous on the counter, but they fell behind just before the half-hour mark when Paco Alcacer's cross was fumbled into the path of Suarez by Ivan Cuellar, allowing the former Liverpool hitman to scramble the ball over the line.
The hosts were almost level in the 35th minute when Amrabat picked out Alexander Szymanowski on the edge of the box, giving him the time and space to get a shot away, but Barca goalkeeper Marc-Andre ter Stegen kept him out at full stretch to maintain his team's advantage.
Barcelona lived dangerously early in the second half, with Leganes threatening an equaliser on more than one occasion, but they extended their lead on the hour mark in similarly scrappy circumstances.
Substitute Aleix Vidal's initial strike was parried by Cuellar, but only as far as Suarez, allowing him to drill home his and Barca's second to give the table-toppers some breathing space.
Leganes looked deflated after the second goal went in, coming undone for the final time in the 90th minute when Lionel Messi's cutback was slid home by Paulinho to cap off the win.
The result leaves Barcelona 11 points clear of bitter rivals Real Madrid ahead of Saturday evening's crucial Madrid derby, and seven ahead of second-placed Valencia in the standings.