The reigning champions had already reached their second successive final by the end of the second day against Argentina when they took an unassailable 3-0 lead. So, although they lost their two rubbers yesterday, it was of no consequece as they completed a 3-2 win.
By contrast, the outcome of the match between Serbia and Canada came down to the final rubber.
Canada started day three leading 2-1 but world No 1 Novak Djokovic completed a straightforward victory over Milos Raonic 7-6 (7/1), 6-2, 6-2 to set up a winner-takes-all clash.
Tipsarevic is ranked 18 places ahead of the Canadian at 23rd in the world but on Friday he twice squandered a one-set lead as Milos Raonic claimed victory with a 10-8 final set.
He had no such difficulties yesterday as he completed a 7-6 (7/3) 6-2 7-6 (8/6) victory over Pospisil to send Serbia into the final in November.
Joining Great Britain in the World Group next year after winning their play-offs are 28-times winners Australia, who returned to the elite level of the competition for the first time since 2007 following a 4-1 win in Poland. Also through are Netherlands, who beat Austria 4-0, Germany, who beat Brazil 4-1, Japan, who beat Colombia 3-2, Switzerland, who beat Ecuador 4-1, Belgium, who beat Israel 3-2 and Spain, who thrashed Ukraine 5-0.
Bernard Tomic secured the Australian win in Warsaw as he defeated Lukasz Kubot 6-4, 7-6 (7/5), 6-3 in the decisive fourth rubber.