That put Barca, cup winners in the past three years, 2-0 up on aggregate in the semi-final second leg in Valencia, before Ivan Rakitic added another.
Coutinho's first goal for Liverpool came in their 5-0 win over Swansea City in January 2013, with Suarez setting him up. The Brazilian ace who left Liverpool to join Barcelona last month in a deal worth £142m found a superb cross from former Anfield favourite Luis Suarez to slot it past the goalkeeper into the left corner.
Barcelona went on to win the match 2-0 and will now advance to the Copa del Rey final after winning 3-0 on aggregate.
Barça now progress to the Copa del Rey final in April where they will face Sevilla in a bid to retain the title they won a year ago. A verdict on the location of the 2018 Copa del Rey final is due to be placed on Monday.
He continued: 'It's a special moment.More news: No. 3 Official at Justice Department to Resign
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"I'm very happy, given it'll be the fifth consecutive Final for these players, something that's very hard to repeat and repeat".
"I was looking for the goal in the first few games and today I got it and, most importantly, helped the team reach the final".
"We're really happy to reach the final". Had the Valencia star been wheeling away in celebration then this game would have been an entirely different one.
Watch Coutinho's first goal down below. But we saw it very clearly, we had to try to move the top part a bit. I am starting to learn how the team works, how Barca works.
The stop proved pivotal as, with eight minutes left, Suarez stole back possession and fed Rakitic, who fired home from just inside the box to safeguard the win.
Having topped their group before Christmas, Barcelona face Chelsea in the round of 16, with the first leg at Stamford Bridge on February 20.