Lionel Messi released Neymar to send in a floated cross from the left and Suarez was on hand to crash home a superb volley.
It brought the Uruguay striker to three figures for the La Liga champions in all competitions, a land mark he has stormed to in 120 appearances, and it was somewhat fitting that he combined with his forward colleagues to do so.
Messi and Neymar were not to be left out of the party either, as the Brazilian netted from the spot before La Pulga hit a stunning free-kick to assure victory.
Barcelona's celebrated MSN front three now have 302 goals since they started playing together in 2014. Messi leads the way with 125, while Neymar has contributed 77.
The strike against Bilbao, which pulled Barcelona level at 2-2 on aggregate in the last-16 tie, was his eighth in 12 Copa del Rey outings.
Suarez has 68 goals in 78 LaLiga matches, with 17 in 24 for Barca in the Champions League.
The rest of his haul comes from a goal apiece in the Supercopa de Espana and UEFA Super Cup and five across a pair of appearances when Luis Enrique's men won the FIFA Club World Cup in 2015.