Moreno cancelled out Kike Garcas first-half opener when the Spain striker cut back in the 63rd minute to shake off his marker and scored from a tight angle.
Moreno also passed for Alcacer to round the goalkeeper and slot home for the winner in the 70th in Villarreal's stadium, which was empty of fans like all Spanish stadiums due to the coronavirus pandemic. The goal was awarded after a video review overturned an initial offside ruling.
Moreno also scored in last weekends 1-1 draw against Huesca, the debut for Emery in his return to Spanish football after stints at Paris Saint-Germain and Arsenal. Previously, Emery had successful runs at Spanish clubs Valencia and Sevilla.
Villarreal reinforced its squad in the short offseason, bringing in former Valencia midfielders Dani Parejo and Francis Coquelin and taking young forward Takefusa Kubo on loan from Real Madrid.
The aim for Villarreal is to crack the top four to earn a Champions League spot after finishing fifth last season and going to the Europa League.
Later, Valencia visits Celta Vigo and Getafe hosts Osasuna.