Both went into the fight unbeaten in 16 professional bouts and Pajkic floored Fury with a huge right in round two.
But the Briton put Pajkic down in the next, and much to the Canadian's anger the fight was ended soon afterwards.
Earlier, former world champion Chris Eubank's son, Chris Eubank Jr, stopped Lithuanian Kirilis Psonoko in round four of his professional debut.
The main bout at Event City in Trafford Park was a frenetic encounter with both men swinging wildly and the aggression extending to the crowd, where there was a brief disturbance.
When Fury momentarily let his guard down in a thrilling second round Sarajevo-born Pajkic, 34, seized his opportunity with a brutal right hook that landed squarely on the chin.
Fury muscled his way back in round three, forcing his opponent into a standing count and taking control, although referee Marcus McDonnell seemed to end the contest rather too hastily with an incensed Pajkic ready to continue.
"I got myself a shock there for sure," 6ft 9 Mancunian Fury said of his second-round knockdown. "He got me with a good shot, but I got up and stopped him.
"To be honest my legs felt strong as soon as I got back up. I was alright. It takes a true champion to get knocked down like that and get back up. It shook up the brain but I need a bit of shaking up to wake up."
Fury's promoter, Mick Hennessy, revealed that the 23-year-old's next bout would be in Blackpool on 28 January, followed by a fight in New York's Madison Square Gardens, on St Patrick's Day, 17 March.
Earlier on the bill, Eubank junior was accompanied to the ring for a six-round contest by his father, to the same "Simply The Best" anthem by Tina Turner that the older Eubank used to walk out to.
The 21-year-old prodigy was fleet of foot and stylish, gradually wearing down the stubborn Psonoko, who maintained a high defensive guard throughout.
"It's been my dream ever since I was a young teen. There's a lot to live up to but it makes me want to work harder to prove myself," said Eubank Jr.
His father added: "It was an almost perfect performance, the opponent was difficult to hit and that will give my son the experience needed."