Gakpo had failed to score in six previous appearances for Jurgen Klopp's side since a £44m move from PSV Eindhoven in January.
But it proved seventh time lucky for the 23-year-old as he was on hand to slot home the insurance goal at Anfield as Liverpool won for the first time in the top flight this year.
Renowned for his goals and assists in his homeland, the pressure had been building on Gakpo to deliver the goods for Klopp's faltering side and scoring for the first time at Anfield has brought a huge relief for Liverpool's number 18.
“It feels amazing to get my first goal in this game – also an important one. I'm really happy. It was amazing," Gakpo told Liverpool's official website.
"Obviously for a striker it's always nice to score and then also in a derby is a really great feeling.
"It's always difficult to come out of the dressing room, and if we start off with a goal, that's amazing. It was a good pressing situation from us – Robbo [with a] good one-two with Hendo, Mo on the ball, a good cross, little deflected, but I was there at the second post.”
Mohamed Salah opened the scoring for Liverpool before Gakpo sealed the win over Sean Dyche's side.
Gakpo will hope to continue his goal contributions against Newcastle United this weekend.