It was the first time the Brazilian had found the net since his blockbuster 160 million-euro ($192 million) move from Liverpool in early January.
Gabriel Paulista lost the ball to Suarez who ran clear to find Rakitic on the edge of the area and the midfielder made no mistake in firing past Jaume to seal Barca's place in the final.
The Brazil global, a €160million signing from Liverpool last month, came off the bench at Mestalla to break the deadlock as Barca claimed a 2-0 win over Valencia and a 3-0 aggregate triumph.
"It's a very happy day", he told GOL. He replaced Andre Gomes at halftime following an entertaining first half in which Valencia striker Rodrigo Moreno was close to levelling the tie with a header that bounced off the crossbar and with another shot well saved by Jasper Cillessen in the Barca goal.
Barcelona reached their fifth consecutive final to be the first Spanish club in the history to make such an achievement. "I finally got it today and it helped the team advance to the final".More news: India hopes to see Palestine becomes sovereign soon: PM
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Winners of the trophy in each of the last three campaigns, the Catalans will face Sevilla in the final set for the weekend of 21 and 22 April.
"I really want to win big titles, it was one of the reasons that made me sign for the club".
Boss Ernesto Valverde said in quotes reported on AS: "Barca are used to reaching and playing the finals".
Trailing 1-0 from the first leg after Luis Suarez's strike separated the teams at the Camp Nou last week, Valencia nearly levelled the tie on aggregate early on.
Still just one goal down, Valencia almost got the equaliser on an outstanding header by Rodrigo that beat Barça net minder Jasper Cillessen but clanked off the crossbar.
The defender was seen grimacing and holding the injured knee at times during the match and was eventually substituted, allowing Colombian Yerry Mina to come on for his debut.