The on-loan Borussia Dortmund man was handed a start in Cardiff, joining Alvaro Morata and Suso in attack and continued his fine form as he found the breakthrough with just eight minutes on the clock.
Suso's cross was punched only as far as Jose Luis Gaya, with his drilled effort being cushioned in the path of Alcacer either by luck or judgement by Dani Ceballos, with the striker then taking a touch before rifling into the top corner from just inside the box.
The goal was Alcacer's first for his country since October 9, 2015 and he didn't have to wait long for his second as he struck again before the half-hour mark.
Captain Sergio Ramos had already doubled the lead with a standard header from a free-kick and Alcacer made is three after Wales failed to deal with a high ball, with Harry Wilson and Joe Allen getting in each other's way.
In the end, the former manager only to prod the ball back into the danger zone, where Alcacer reacted quickest to volley home low first time for his second of the game.