Torres continued his fine form in front of goal with a devastating display that booked La Roja’s place in the Nations League finals at their opponent’s expense.
He crashed an unstoppable volley home to put Spain 2-0 up after half an hour in Seville and Rodrigo extended their lead before half-time with a glancing header from a corner, all after Alvaro Morata had opened the scoring.
Torres got his second and Spain’s fourth when he tapped in from close range having been picked out at the far post by former Valencia team-mate Jose Gaya and the City youngster sealed his hat-trick with a composed 18-yard strike to make it 5-0.
Ilkay Gundogan was on the receiving end of his team-mate’s heroics, playing the full 90 minutes for Germany as Mikel Oyarzabal completed the rout late on.
In Split, it proved to be an equally memorable night for Dias, who was the match winner in Portugal’s last gasp 3-2 win over 10-man Croatia.
The centre-back reacted quickest to fire a 90th minute winner into an unguarded net after the home side’s goalkeeper, Dominik Livaković, spilled a cross.
Dias already had reason to celebrate, having netted his first senior international goal shortly after half-time.
Again, the 23-year-old showed good instincts in the penalty area, poking home from six-yards after Ruben Semedo picked him out following Cristiano Ronaldo’s dipping free-kick.
Joao Cancelo and Bernardo Silva were both involved for Portugal, coming off the substitutes bench for the final 19 minutes, but the night belonged to their new team-mate.
Brazil impress again
Brazil continued their 100% start to their South American World Cup qualification phase with a 2-0 win in Uruguay.
Ederson again got the nod in goal and Gabriel Jesus played the full 90 minutes as the Selecao scored twice before the break through Arthur Melo (34) - assisted by Jesus - and Everton striker Richarlison (45).
Manchester United's Edinson Cavani was shown a straight red after a VAR review for a nasty challenge on Richarlison.
Brazil top the group with maximum points from four matches.
The top five teams from the 10-nation group will qualify for Qatar 2022.