Cristiano Ronaldo cancelled out an early header from Jeremy Mathieu just before Suarez struck to leave the actual hosts four points clear presents itself La Liga.
Although Barca manufactured the brighter start, Real soon found myself in the game and had the very first big chance when Karim Benzema's cross found Ronaldo unmarked on the far post, but he did not have much angle to cooperate with and could only send his cushioned volley contrary to the crossbar.
Barca then went onward after Suarez won a free-kick, Lionel Messi swung it into the middle and French centre-back Mathieu showed up unmarked to send a perfectly placed header at night dive of Iker Casillas.
But Real battled quickly back and a dramatic minute saw Suarez's cross-shot present Neymar which has a golden chance which he place straight at Casillas, before Real immediately broke and also Benzema's brilliant backheel found Ronaldo to get a low stabbed finish.
Real finished the opening period in the ascendancy as Gareth Bale had a goal disallowed for a marginal offside and Ronaldo forced a good save from Claudio Bravo with a thunderous long-range drive.
The visiting team made a similarly strong start to the second half with an early chance for Benzema saved. But Barca then re-established the advantage with a decidedly route one goal as Brazil right-back Dani Alves delivered a long ball over the top, Suarez produced brilliant control and then steered a perfectly placed low finish into the bottom left corner.
The home team were dominant after that, squandering several chances to double their lead as Neymar ended a brilliant run by shooting over and then thrashed a shot wide after a pass from Messi, while Casillas did well to save from both Messi and Jordi Alba.
Real had little answer and, aside from a deflected strike from Benzema which Bravo did well to save low to his left, they never seriously threatened an answer as a jubilant Nou Camp celebrated a well deserved win.
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