Australia, Germany and Italy were among the 12 nations to book their place in the inaugural Davis Cup Finals after winning their qualifying matches.
European nations Belgium, Serbia and the Netherlands also made it through, while Russia upset Switzerland on their way to the Finals.
Kazakhstan, Colombia, Chile, Canada and Japan will also be involved in the 18-nation Finals, which take place in Madrid in November.
In a revamp of the previous Davis Cup format, the qualifiers join last year's semifinalists France, Spain, Croatia and the United States and wildcards Britain and Argentina for the one-off World Cup style event.
The Australian team managed a 4-0 sweep of Bosnia and Herzegovina as John Millman, Alex De Minaur and Alexei Popyrin all won their singles matches in the absence of Nick Kyrgios and Bernard Tomic, whose long-running feud with coach Leyton Hewitt meant he was not involved.
Italy were dominant in their singles matches against India as Andreas Seppi and Matteo Berrettini secured a 3-1 victory in Calcutta, while top seeds Belgium also won 3-1 away from home with Kimmer Coppejans securing two singles points to help defeat Brazil.
Serbia -- without Australian Open winner Novak Djokovic -- were given a scare by Uzbekistan before Filip Krajinovic won the deciding singles match against Sanjar Fayziev to put his nation through 3-2.
Switzerland were also missing key players Roger Federer and Stanislas Wawrinka and it showed against Russia as dangerous youngsters Karen Khachanov and Daniil Medvedev proved too strong in the singles during their 3-1 win.
Elsewhere Kazakhstan's Mikhail Kukushkin won two matches in his nation's 3-1 win over Portugal, Robin Haase was involved in singles and doubles wins as Netherlands defeated Czech Republic 3-1 and the team from Colombia did not drop a set as they beat Sweden 4-0.
Chile came back from 2-1 down against Austria to win 3-2 thanks to singles wins for Nicolas Jarry and Christian Garin, Canada's Denis Shapovalov was instrumental in their 3-2 away win in Slovakia and Taro Daniel won a tense final singles berth to secure a 3-2 win for Japan over China.