The heavily favoured Canadians needed five sets to defeat Japan's Go Soeda and Yasutaka Uchiyama 7-5, 2-6, 6-3, 3-6, 6-3 to give Canada a 2-1 lead in the best-of-five tie.
Nestor, an Olympic gold medallist and Wimbledon doubles champion, admitted he became impatient during the match. Neither of the Japanese players are ranked among the world's top 250 players in doubles.
"You are playing Davis Cup and you have to expect they are going to play their best," said the Toronto native, who is ranked No. 5 in doubles.
"Sometimes I get a little frustrated because you want to go more straight forward. There is a reason you are ranked higher and you want them to fold. That doesn't happen."
Canada needs to win just one of the two singles matches Sunday to advance to the world group quarter-finals for just the second time.
Canadian ace Milos Raonic of Thornhill, Ont., can win the tie when he faces Japan's top-ranked player Kei Nishikori. Raonic is ranked sixth in the world while Nishikori is fourth.
The other singles match has Pospisil, of Vancouver, scheduled to play Tatsuma Ito.
Canadian coach Martin Laurendeau said his team is where it wanted to be.
"You have one more match to win but it's often the toughest one," said Laurendeau. "Everyone would rather be up 2-1 than down 2-1.
"Hopefully it allows Milos to breathe a little easier and lets him begin the match a little more relaxed so he can be loose and play the game a little bit more comfortably."
Laurendeau wasn't surprised by the fight shown by Soeda and Uchiyama.
"It's Davis Cup, guys come out swimming," he said. "When you are the underdogs, one of the ways to approach the match is go for the win. You have everything to gain."
The fifth and deciding set was a nail biter.
Canada needed a line call on a Japanese shot to win the fifth game and take a 3-2 lead. Uchiyama delivered an ace to win the next game and tie it 3-3.
Canada won the next game when Uchiyama returned Nestor's serve into the net. Soeda then double-faulted to put Canada ahead 5-3. Nestor won the match with a forehand shot that neither Japanese player could return.
The match had the atmosphere of a hockey game with Canadian flags waving and drums pounding. Some fans among the noisy crowd at the Doug Mitchell Thunderbird Sports Centre on the University of British Columbia campus showed up with painted faces and waved large cardboard cut-outs of their favourite players. A contingent of Japanese fans cheered each time Soeda and Uchiyama scored a point.
"It was great atmosphere," said Pospisil. "It was a little bit of a rollercoaster match.
"We used the crowd really well."
Soeda, who is ranked 82nd in the world in singles, found small consolation in pushing the Canadians in the three-hour match.
"I'm very disappointed," he said through an interpreter. "You lose, you lose."
There was speculation coach Minoru Veda might use Nishikori in the doubles match.
"That was considered," Veda said. "I made the order and I stuck with that."
Canada and Japan split their singles matches on Friday's opening day of competition.
Raonic defeated Ito 6-2, 6-1, 6-2. Japan moved into a tie when Nishikori defeated Pospisil 6-4, 7-6, 6-3.