Holders Switzerland crashed out of the Davis Cup in the first round on Sunday with Belgium advancing 3-2 to the quarter-finals.
David Goffin, competing for the first time this weekend after suffering a back problem, sealed the winning point by beating Adrien Bossel 6-4 6-0 6-4.
Switzerland, missing big guns Roger Federer and Stan Wawrinka, had earlier levelled 2-2 after Henri Laaksonen survived a five-setter against Steve Darcis 6-3 3-6 3-6 7-6 (7-5) 6-1.
Belgium next play either Canada or Japan, with the Canadians leading 2-1 in Vancouver.
The Swiss, who won the Davis Cup for the first time last year beating France 3-1 in Lille, will now compete the World Group play-offs on September 18-20.
Belgium's best previous performance was finishing runner-up in 1904, although more recently the reached the semi-finals in 1999.
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