Germany beat Belarus 4-1 while Colombia beat Argentina in a South American derby.
Italy thrashed South Korea 4-0 in Cagliari in a tie with no fans because of the coronavirus scare.
And Lleyton Hewitt’s Australia beat Brazil 3-1 in Adelaide as the USA defeated Uzbekistan.
Playing their final Davis Cup match, Bob and Mike Bryan secured USA’s place in Madrid with a 6-3 6-4 win over Sanjar Fayziev and Denis Istomin in the third rubber.
Kazakhstan meanwhile, will be in Madrid for the second year after beating the Netherlands.
2016 champions Argentina failed to qualify after going down 3-1 to Colombia in Bogota.
Daniel Elahi Galan delivered the decisive win, beating Juan Ignacio Londero 6-3 6-4.
Ecuador, Sweden, Hungary, Czech Republic and Austria will all be in the draw next week for the 18-nation showdown in November.
Ecuador thumped Japan 3-0 in Miki but the hosts were without injured Kei Nishikori and world No.48 Yoshihito Nishioka.
In an empty stadium, Gonzalo Escobar and Diego Hidalgo secured the winning point in a decisive doubles victory over Ben McLachlan and Yasutaka Uchiyama for the South American nation.
Sweden, who won the Davis Cup seven times between 1975 and 1998, beat Chile 3-1 and Hungary, who will host Fed Cup finals this year, won a thriller over Belgium 3-2.
The Hungarians were trailing 2-1 after Saturday’s doubles, but fought back with singles wins for Attila Balazs and Marton Fuscovics.
Nearby, the Czech Republic beat Slovakia 3-1 with Czech No. 1 Jiri Vesely the hero as he beat Andrej Martin 4-6 7-5 7-5.
Austria, without Dominic Thiem, beat Uruguay in Graz as Dennis Novak knocked off Pablo Cuevas to give his side a 3-1 win.
Marin Cilic led Croatia past India in Zagreb, but not before veteran duo Leander Paes and Rohan Bopanna edged Mate Pavic and Franko Skugor in Saturday’s doubles.
Last year’s winners Spain, runners-up Canada and losing semi-finalists Britain and Russia, as well as wildcards Serbia and France did not need to play in the qualifiers.
Doping sanction victim Simona Halep has gone online to protest her own treatment by anti-doping…
Rafael Nadal lined up for what was to be the final match of his career…
Jannik Sinner took charge in front of his home crowd on Sunday, crushing ATP Finals…
Daniil Medvedev went into meltdown mode on Sunday during a highly charged 6-4, 6-3 loss, with opponent…
Jannik Sinner could well be missing from the opening European clay event of next season…
Rafael Nadal will bring down the curtain on his career next month as he plays his…