The 25-year-old Brazilian broke the deadlock in the 49th minute of the second leg clash at Mestalla, having only entered the fray at the start of the second half.
Ernesto Valverde's decision to send him on in place of Andres Gomes reaped instant dividends. Coutinho stole in behind the Valencia defence to turn in a Luis Suarez cross at the back post. The strike made it 2-0 on aggregate to the Catalans.
Ivan Rakitic swept home Barcelona's second goal on the night eight minutes from the end to give them a 3-0 aggregate win.
"For me it is my first final, so it is a very special moment," Coutinho, who moved to Catalonia from Liverpool for 160 million euros in January, told the TV station Gol. "I am very happy. I had been searching for this goal in my first few matches. I got it and it helped the team get through to the final."
Barcelona will take on Sevilla in the final in April.
Valverde's men are attempting to win the trophy for the fourth year on the trot and thereby emulate the Athletic Bilbao sides who claimed four titles between 1930 and 1933.
Valencia had been hoping to reach the final for the first time since they won the cup under Ronald Koeman in 2008.