Suarez scored his second of the game with a cute panenka effort to make the score 3-0 and send Barcelona into the final.
It came in the 72rd minute with Real Madrid already looking dead and buried and then finished any late hope they may have had.
A strange Clasico, ahead of another this weekend, saw Real Madrid create plenty of chances but fail to convert as Barcelona ended up running riot at the Bernabeu.
And Barcelona fans failed hailed the Uruguay striker after his final goal rubbed salt into the Madrid wounds.
“Suarez has no expiration date,” wrote on fan.
Another said: “The best will be recognise in to the best match ,so never criticize Luis Suarez again…ez”
Another said: “Suarez’s penalty was just disrespectful.”
And another wrote: “SUAREZ MAKES IT 3-0. TRASH LAST WEEK, GENIUS PANENKA THIS WEEK.”
Barcelona will face the winner of the Valencia and Real Betis clash with the second leg tomorrow with the score at 2-2.
Suarez scored twice, either side of Raphael Varane’s own goal, to send Madrid packing and all but end their hopes of a trophy this season.
Madrid are trailing in the league with Barca nine points clear of their rivals – and seven ahead of Atletico.
Real Madrid vs Barcelona – how it happened
A clinical Barcelona beat Real Madrid 3-0 away in an intense Copa del Rey semi-final, second leg on Wednesday as a Luis Suarez double helped them secure a 4-1 aggregate victory and a spot in the final for the sixth straight season.
A dominant yet wasteful Real ravaged their rivals in the first half while spurning a string of clear chances at the Santiago Bernabeu.
Yet Barca went ahead against the run of play in the 50th minute as Ousmane Dembele led a counter-attack and Suarez slotted his pass into the net.
Spearheaded by the pace and confidence of Brazilian teenager Vinicius Jr, Madrid continued to fly forward but failed to find the target.
Barca effectively killed off the tie when Raphael Varane bundled the ball into his own net as he tried to prevent Suarez reaching another cross from Dembele.
Suarez then earned a penalty and further humiliated Madrid by converting with an audacious ‘Panenka’, deceiving goalkeeper Keylor Navas by chipping the ball into the net.
La Liga leaders Barca will visit Real again in the league on Saturday.
The Catalans, who are bidding to win the trophy for a record fifth consecutive year, will play either Real Betis or Valencia in the final on May 25 at Betis’ Benito Villamarin stadium.
Valencia host Betis in their second leg on Thursday, having drawn 2-2 in the first leg.
Barca coach Ernesto Valverde attempted to neutralise the threat of Vinicius by deploying right-sided defenders Sergi Roberto and Nelson Semedo to protect the left flank but the Brazilian was still the most dangerous player in the first half.
Vinicius could have won a penalty when Semedo clattered into him and had three clear chances to score before the interval, failing to hit the target twice from inside the area, and being thwarted by Marc-Andre Ter Stegen.
He continued to dance his way through Barca’s defence after the break but his final touch let him down.
Shortly after Suarez’s opener, he cut into the box and delivered a cross which Sergio Reguilon met with a diving header, but Ter Stegen flew across his goal to repel the effort.
Madrid, who were also beaten 3-0 by Barca at the Bernabeu in La Liga last season and were thrashed 5-1 by their rivals back in October, lost their heads after that chance and there was no coming back following Varane’s own goal.
Barca seemed to relish their role as Real’s tormentors and Suarez took the ball from usual penalty taker Lionel Messi to complete their fourth victory in five visits to the Bernabeu with an ice-cool finish from the spot.