However, the numbers soon caught up with Barcelona as Gareth Bale hit an equaliser in the 72 minute. Real Madrid's response came only five minutes later when Cristiano Ronaldo tucked-in a goal to a brilliant header by fellow Karim Benzema.
Instead of kicking the ball out of play, however, Real Madrid held on to possession.
Suarez missed an early chance after being fed by Messi, but the Uruguay forward put Barca in front in the 10th minute. The flick went toward the net and found Ronaldo, who tapped it past Marc-Andre ter Stegen.
Ronaldo added a goal of his own and gave Madrid's fans a scare when he couldn't play on through a leg injury and needed to be substituted at halftime.More news: Hezbollah hails Lebanon election vote as 'great victory'
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If Real Madrid had played all season like they did against Barcelona in the Clasico on Sunday, they would still be challenging for La Liga.
Ramos revealed that he may follow the footsteps of departing FC Barcelona legend, Andres Iniesta who had announced his retirement at the end of the season.
FW Lionel Messi, 8 - Only the Argentine is capable of the skill and shooting ability he demonstrated for his goal, fending off Sergio Ramos and Casemiro before rifling into the bottom corner.
Marcelo also thought Jordi Alba fouled him in the Barcelona 18-yard box in the 76th minute, but the referee opted against awarding the penalty.
In particular, the Spanish global was not happy with Lionel Messi and Luis Suarez.
Messi looked poised to get another goal but Bale made it 2-2 by using one touch to curl Asensio's pass around Ter Stegen.