The striker's superb performances on loan at Borussia Dortmund earned him a call-up and he continued that form with a first-half brace for his first international goals since 2015.
Sergio Ramos converted a Suso free-kick in between Alcacer's double and Marc Bartra's header wrapped up Spain's scoring as they brushed a lacklustre Wales aside at the Principality Stadium.
With Gareth Bale not fit to play, Ryan Giggs was shorn of his star man and Wales rarely looked like threatening a surprise result, although Sam Vokes did net a late consolation.
Alcacer opened the scoring in the eighth minute on his first international appearance since 2016, arrowing a powerful drive into the top-left corner after Wales failed to clear following a punch from goalkeeper Wayne Hennessey.
And Hennessey's goal was soon breached again, with Spain skipper Ramos left completely unmarked to head home a floated free-kick by Suso after Alvaro Morata was fouled.
Alcacer was celebrating again in the 29th minute, capitalising on more chaotic defending to beat Hennessey with a sweetly struck low volley, although Ethan Ampadu's looping header hit the outside of David de Gea's post in a rare Wales attack.
Suso almost added a fourth after the break but his 25-yard curler clipped the crossbar, before Morata headed wide a left-wing cross from Jose Gaya.
More slack Wales marking was punished by Bartra's flicked header from a Suso corner and, despite Vokes untidily finishing off a brilliant David Brooks cross with a minute to play, the final scoreline reflected Spain's dominance.