Spain fought back from a 2-0 deficit to qualify for the Final 8 with a 3-2 win over Denmark in their qualifying tie, while Belgium knocked out 28-times winners Australia.
Germany reached the Final 8 by routing Japan, while France secured a convincing win over Croatia. Argentina knocked out last year's runners-up, the Netherlands.
Should Carlos Alcaraz, the new world number one after his US Open triumph, play for Spain in the Final 8 and with Italy on the other side of the draw, he could face Jannik Sinner in another final this year if their teams get there.
Alcaraz and Sinner have faced each other in five finals this year, including three Grand Slams and two Masters tournaments, with the Spaniard triumphing on four occasions.
The Davis Cup Final 8 takes place the week immediately after the ATP Finals. Both Alcaraz and Sinner have qualified for the event in Turin, which takes place from November 9 to November 16. The Final 8 takes place in Bologna from November 18 to November 23.