Evans recovered from two sets and a break down to lead in the fourth set but Pospisil delighted the raucous home crowd at the TD Place Arena by pulling off a 7-6 (7/3) 6-4 3-6 7-6 (7/6) victory.
The tie will now come down to a meeting between Kyle Edmund, so disconsolate after his loss to Pospisil on Friday, and 17-year-old rookie Denis Shapovalov.
Stand-in British number one Evans went into the clash as the favourite on both form and ranking - 45 to 133 - while Pospisil was publicly wavering about whether to play on Saturday evening because of a knee problem.
But the super-fast court played to his strengths - he served 25 aces and hit 36 forehand winners - and in the end he overpowered his smaller opponent.
Vasek Pospisil of Canada reacts after beating Daniel Evans of Great Britain 4-1 on the third day of Davis Cup first round between Canada and Great Britain at TD Place in Ottawa, Ontario, February 5, 2017. The series is now tied at 2-2.
Image credit: AFP
Pospisil leapt high and threw his racket in the air at the moment of victory, and he said: " It feels incredible. That was definitely the loudest atmosphere that I've played in ever."
The result will be a big disappointment for Evans, who came into the tie in the form of his life after reaching the fourth round of the Australian Open.
This could have been Milos Raonic against Andy Murray but what the match lacked in star power it more than made up for in drama.
Pospisil has plummeted down the rankings from a high of 25 in 2014, winning just 10 tour-level matches in 13 months prior to this tie.
But the 26-year-old still represented Canada's big chance, with his potential replacement Peter Polansky inexperienced at this level.
The strapping on his knee had grown overnight and he made a tentative start. Had Evans taken one of two chances for a double-break lead at 3-1 in the opening set, things may have turned out differently.
Daniel Evans of Great Britain a return against Vasek Pospisil of Canada during the third set the third day of Davis Cup first round between Canada and Great Britain at TD Place in Ottawa, Ontario, February 5, 2017.
Image credit: AFP
But he did not, Pospisil fed off the crowd to level at 3-3 and grew in confidence from there.
The Canadian had been bullish about his chances ahead of the clash, claiming the match was on his racket, and he backed it up on the court.
Evans was driven further and further behind the baseline by Pospisil's fierce serve and forehand and could find no way to change the momentum.
Pospisil played a high-quality tie-break and then blasted another forehand winner to break for 2-1 in the second set.
Although Evans found a fine angled backhand of his own to hit straight back, Pospisil pounced on his serve again for a third straight break.
Evans appeared irritated by shouts from the Canadian bench and exchanged words with the umpire but most of his frustration was directed at his opponent.
Vasek Pospisil of Canada reacts after winning a point against Daniel Evans of Great Britain during the end of the fourth set on the third day of Davis Cup first round between Canada and Great Britain at TD Place in Ottawa, Ontario, February 5, 2017.
Image credit: AFP
Three times he had 0-30, and eventually two break points when Pospisil served for the set, but each time the Canadian used his big weapon to snuff out the chances.
Evans had never come back to win a match from two sets down, and his hopes took another blow when he dropped serve again early in the third.
But Pospisil finally showed that he was, after all, a player lacking confidence as the surety of his strokes began to crumble.
A double fault gave Evans the break back and, when Pospisil finally won another game, he was already a break down in the fourth set.
Evans had chances to make that a double break but, as in the opening set, Pospisil resisted well and then rediscovered his missing spark as he levelled at 3-3.
Only a stunning backhand volley from Evans denied him the chance to serve for the match, and the Birmingham player led 4-2 in the tie-break.
But the final twist was a run of four points in a row for Pospisil, who then clinched victory on his second match point when Evans' return sailed wide.
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