Canada and Japan were tied at 2-2 heading into the final rubber after Kei Nishikori beat Milos Raonic 3-6, 6-3, 6-4, 2-6, 6-4 to keep the tie alive for Japan.
However, Pospisil was not overawed by the occasion and dispatched his Japanese opponent to ensure Canada set up a quarter-final clash with Belgium in July.
Even though the pressure seemed to be getting to Pospisil initially, he managed to hold on to win the first set 7-5. From there he started to find his feet and gain a lot more confidence, which spelt the end for Soeda.
In the match featuring Raonic and Nishikori, the world number six started off well as he won the first set 6-3.
However, Nishikori, who is ranked fourth in the world, bounced back to win the next two sets.
With his back to wall and so much at stake, Raonic refused to go down without a fight as took the fourth set 6-2 to send the match into a decider.
Unfortunately for Raonic, he could not keep up the momentum as Nishikori counter-attacked with a vengeance to win the match in three hours and four minutes.
Canada had taken the early initiative as they went 1-0 up after the opening rubber as Raonic beat Tatsuma Ito 6-2, 6-1, 6-2.
Japan levelled matters at 1-1 when Nishikori beat Pospisil 6-4, 7-6 (7-5), 6-3 in the second rubber.
In the doubles section of the tie, Daniel Nestor and Pospisil were made to fight hard for their 7-5, 2-6, 6-3, 3-6, 6-3 win over Soeda and Yasutaka Uchiyama.