Thriving in a partisan atmosphere similar to the one that carried Serbia to a 3-2 victory over France in the 2010 final, Djokovic crushed Pospisil 6-2 6-0 6-4 before the towering Raonic hit 34 aces to outgun Tipsarevic 5-7 6-3 3-6 6-3 10-8.
"It's always great to win a Davis Cup match especially in front of a home crowd because you represent your country and I can say that it's been a fantastic performance for me given that I only got here 48 hours ago," Djokovic told a news conference.
"There is a possibility I might play in the doubles tomorrow but team captain Bogdan Obradovic will have the final say. Either way this win will have boosted my confidence and the overall team spirit."
The 22-year-old Raonic appeared set for a quick stroll after blasting 11 winners to race into a 3-0 lead in the opening set but then started to misfire as the home favourite regained his composure.
Roared on by 10,000 passionate fans, Tipsarevic rallied to take the set and although his opponent recovered to claim the second, the Serb wore down his opponent in the third with a barrage of stinging baseline shots on the indoor red clay.
The heavily-tattooed Tipsarevic had the crowd on its feet with a delightful drop volley in the closing stages of the third set and sealed it with a rare ace as an ancient Serb battlesong blared out between games to create an electrifying atmosphere.
Tipsarevic, 29, lost his grip on the match in the fourth set when he directed an easy smash at Raonic who broke serve and then held his own, unleashing three aces in a row to level.
With the pair trading shots like a pair of heavyweight boxers, games went with serve in the fifth set until Montenegrin-born Raonic, who saved a match point in the 10th game, produced a series of aces and service winners.
Earlier, Djokovic looked a little weary in the opening three games after a long-haul flight from New York following his U.S. Open final defeat by Rafael Nadal but it was one-way traffic once he found his feet against Pospisil.
Having trailed 2-1, a fired-up world number one claimed 13 games in a row.
Djokovic won an impressive 12 out of 14 points at the net and celebrated many of his winners with a clenched fist while letting out a trademark primal scream or two.
A small but vociferous band of visiting fans, waving large Canadian flags, cheered every winning shot Pospisil mustered but Djokovic wrapped up victory when his opponent slammed a forehand into the net.
Asked what kind of challenge he expected against Raonic in Sunday's opening reverse singles, Djokovic said: "A tough one because he has the potential to storm into the top five (of the world rankings) very soon.
"He has a big serve and one of the strongest pair of calf muscles I have ever seen."
The winners will play holders Czech Republic or Argentina in the November 15-17 final.
- Sports & Recreation