Nestor and Pospisil let a two-set lead get away and then emerged with the critical victory that moved the Canadians to within one match victory of a spot in the semifinals.
The doubles team from Canada defeated Daniele Bracciali and Fabio Fognini 6-3, 6-4, 3-6, 3-6, 15-13 in a match that went on for 4 hours, 27 minutes.
The Canada-Italy doubles confrontation was almost an exact copy of a match played earlier in the day in the United States-Serbia series.
The Canada-Italy winner will meet the United States-Serbia survivor in the semifinals.
Canada's Milos Ranoic will try to clinch the semifinal spot in Sunday's opening singles match against Andreas Seppi. A win by Seppi in that match would leave it all on the line in the fifth and final match of the series between Pospisil and Fognini.