Messi found Gomes out wide on the right, who laid the ball on a plate for Neymar to tap home at the back post – although he looked to have been offside.
Messi then set up Alcacer, three minutes into added time at the end of the first half, after a mazy run into the box, who netted with a cool finish, low and in the corner.
Gomes came close to a goal for Alaves with his 47th minute free-kick, while Pacheco denied Alcacer at his far post after the attacker was played through by Messi.
Alcacer poked a 57th minute effort over the bar as Ivan Rakitic smashed over from 25 yards.
Gomes blocked a shot from substitute Ruben Sobrino before Cillessen’s foot stopped Deyverson from scoring from close range after his initial header on goal was deflected back into his path late on.
Barca looked to wind down the clock for the remainder of the game, and despite giving it their all, Alaves had to settle for defeat as Enrique signed off his Barcelona tenure with the Copa del Rey trophy.