Former winners Australia, Germany and Serbia were among 12 qualifiers that secured their places in the revamped Davis Cup finals which will take place in Madrid in November.
They will join the four teams that contested the semis-finals last year - holders Croatia, finalists France, Spain and the United States - as well as wildcards Britain and Argentina, in the 18-team competition that has divided the tennis world.
Australia routed Bosnia and Herzegovina 4-0 with John Peers and Jordan Thompson winning the doubles before teenager Alexei Popyrin won his Davis Cup debut in the dead rubber.
Germany, who completed a 5-0 rout of Hungary, are the only country represented by a player in the world's top 10 at this weekend's qualifiers.
World No.3 Alexander Zverev and Philipp Kohlschreiber repeated more singles success after the pairing of Tim Puetz and Jan-Lennard Struff brushed aside Hungarians Gabor Borsos and Peter Nagy 6-2 6-3 in the doubles.
"Our captain told us before the match to go for every shot, to be ready to avoid that they start playing very well and to be aggressive in our service games and our return games," Struff said.
"That was the key."
Serbia squandered a 2-0 lead against Uzbekistan after Sanjar Fayziev and Denis Istomin clawed a point back in the doubles and Istomin beat Dusan Lajovic in his singles rubber in Tashkent to level the tie at 2-2.
It was left to Filip Krajinovic to mount a rescue, which the Serb duly did with a 4-6 6-3 6-0 win over Fayziev to send his team through.
Canada's teenage duo of Denis Shapovalov and Felix Auger-Aliassime triumphed on hostile clay in Slovakia to send the Canadians through as 3-2 winners.
Switzerland were dumped out 3-1 by the Karen Khachanov-led Russia, Japan edged China 3-2 while others to advance were the Netherlands, Belgium, Italy, Kazakhstan, Chile and Colombia.
