The Canadians advanced to a September semifinal against Serbia, which defeated the United States on Sunday.
Canada has never been in the world group semifinals since the current Davis Cup format began in 1981. Canada did reach a semifinal in 1913, losing to the U.S.
Canada took a 2-1 lead when Daniel Nestor and Vasek Pospisil teamed up for a five-set decision over Fabio Fognini and Daniele Braccaili on Saturday.
It was Raonic's second win of the weekend, having opened the series with a singles victory over Fognini.