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 were to 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 in the World Group playoffs on September 18th-20th.
Belgium's best previous performance was finishing runner-up in 1904, although more recently the reached the semifinals in 1999.
ROGER FEDERER
Belgians knock Swiss out of Davis Cup tourney
Defending champions Switzerland crashed out of the Davis Cup in the first round on Sunday with Belgium advancing 3-2 to the quarterfinals of the men's team tennis tournament.
Published: 8 March 2015 22:10 CET
Swiss Henri Laaksonen in action on Sunday. Photo: John Thys/Belga/AFP
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