Barca coach Ernesto Valverde may take some of the credit for Coutinho's first goal for the club after taking the decision to bring him on for Andre Gomes at half-time. Suarez drove into the penalty area down the left and crossed towards the far post, where Coutinho stretched to turn the ball back across goal and into the left-hand corner.
Marcelino has urged Valencia to play with their heads as well as their hearts as they attempt to edge past Barcelona into the Copa del Rey final.
And Coutinho's second-half strike, coupled with Rakitic's late goal, was enough for Barcelona to make the final at Valencia's expense.
Barcelona have won the trophy for the last three years and face Sevilla in the final on April 21, a re-run of the 2016 showpiece which the Catalans won 2-0 after extra time.
"I have been trying to score since my first game and I'm happy to have done that, although the most important thing is that the team won the game and we are able to leave here happy".
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Barcelona will have the chance to retain the trophy they won a year ago after a hard-fought win over Valencia at the Mestalla.
Barcelona, however, also owe goalkeeper Jasper Cillessen for the win.
Valencia had centre-back Ezequiel Garay carried off and then saw Cillessen make an incredible save to deny Jose Gaya from point-blank range in the 74th minute.
Valverde later admitted that he was suffering from muscle fatigue having gambled on his fitness at the start of the game.
Valencia had two golden chances in the first half, but Rodrigo's effort hit the woodwork and Francis Coquelin's shot was saved.
A good night all round for Barca was rounded off when Yerry Mina replaced Gerard Pique seven minutes from the end.