Papu Gomez scored twice as Atalanta overpowered Lazio 4-1 in Rome while Serie A title rival Inter Milan crushed promoted Benevento 5-2 on Wednesday.
The two scheduled season-opening matches had been pushed back because of Atalanta and Inter’s European campaigns in August.
Atalanta and Inter are now both top of the Serie A table alongside Napoli, Hellas Verona and AC Milan with a maximum of six points from two games.
Real Madrid missed the creativity of the injured Eden Hazard as only a fortuitous goal from substitute Vinicius Junior earned it a 1-0 victory over Real Valladolid in LaLiga on Wednesday.
Earlier, Atletico Madrid followed up its 6-1 thrashing of Granada on Saturday with a much less spectacular goalless draw away at Huesca.
The results:
LaLiga: Villarreal 3 (Paco Alcacer 13, 67, Gerard 45+1-pen) bt Alaves 1 (Edgar 36); Huesca 0 drew with Atletico Madrid 0; Real Madrid 1 (Vinicius Junior 65) bt Valladolid 0; Eibar 0 lost to Elche 1 (Boye 37).
Serie A: Benevento 2 (Caprari 34, 76) lost to Inter Milan 5 (Lukaku 1, 28, Gagliardini 25, Hakimi 42, Martinez 71); Udinese 0 lost to Spezia 2 (Galabinov 29, 90+4); Lazio 1 (F. Caicedo 57) lost to Atalanta 4 (Gosens 10, Hateboer 32, Gūmez 41, 61).