Barca were nowhere near their fluent best, but ground out their 11th win from 12 games this term regardless.
Suarez broke his five-game goal drought with a scavenger's effort after an Ivan Cuellar error rendered a promising Leganes start redundant, and the hosts' goalkeeper was left helpless by a deflection as the Uruguay international struck again in the second half, with Paulinho tapping in a late consolation.
At the other end, Marc-Andre ter Stegen made a string of saves to preserve the comfortable nature of the scoreline, with half-time substitute Claudio Beauvue missing two fine Leganes openings.
Daunting trips to Juventus in the Champions League and second-placed Valencia next week now await Ernesto Valverde's side, although this victory ensures they will travel to Mestalla sure of keeping top spot.
Leganes were defensively determined and dangerous on the counter-attack, Nordin Amrabat off-target from a raid forward in the 20th minute, but Cuellar's error undid their good work just before the half-hour.
Paco Alcacer's radar was off as he whipped a ball into the area, but Cuellar's attempt to parry clear spun back into danger and Suarez pounced to end his drought.
Barca's joy was almost immediately tempered as Gerard Pique picked up a booking to rule him out of next week's clash with Valencia and Alexander Szymanowski brought a sharp save out of Ter Stegen before the break as Leganes stuck to their task.
Ter Stegen was again called into action when Amrabat sent Beauvue clear seven minutes into the second half, but the Frenchman could only hit the keeper from close-range.
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.
Cuellar could count himself unlucky as he denied Alcacer's shot, only to see the rebound fall to Suarez, whose acrobatic effort was deflected past his own goalkeeper by Ruben Perez.
Ter Stegen smothered Amrabat to deny Leganes again soon after and the difference of luck could be summed up when Pique deflected Szymanowski's cross goalwards, but straight into his goalkeeper's hands.
Beauvue blazed over unmarked from 12 yards as Leganes' hopes of a comeback began to fade and Aleix Vidal failed to mark his return from an ankle injury when he blasted a rebound over, following a blocked Suarez effort.
Cuellar spurned a driven Lionel Messi effort and denied Suarez a hat-trick on the follow-up, but the Argentine's determination, despite a game spent on the periphery, led to the clincher in the final minute, Paulinho prodding in his fourth goal of the season to add a sheen to the scoreline that neither side particularly deserved.
