Jacobs, who also masterminded Canada's success in Sochi in 2014, picked up his second gold medal, as did Marc Kennedy and Ben Hebert - who were both part of Kevin Martin's winning team in Vancouver in 2010.
For Canada, it was a triumphant end to a tumultuous campaign in which they were thrust into the centre of a media storm after being accused of cheating by Sweden during a round-robin game.
The gold was Canada's fourth in men's competition at the Olympics and seventh overall.
Mout shocked
Bruce Mouat's Britain, meanwhile, will go home with another silver medal after faltering at the same stage in Beijing four years ago.
In the build-up to the Games, they were billed as the tournament favourites, a title they earned after becoming the first rink to win four Grand Slams in one campaign in the 2024-25 season. They also won the 2025 world championships.
"I'm just a bit in shock because I felt we were the better team there," Mouat told the BBC.
"Regardless of the result, the amount of people that came out to support us and the messages from back home. We love our sport and if we can take anything away, apart from the silver, it's that we can inspire people to play."
Britain's men's team last struck Olympic gold when curling made its debut as an Olympic sport at the 1924 Games in Chamonix, and have not stood atop the podium since it was added back to the programme in 1998 at Nagano.
Decisive ninth end
Britain made a strong start, limiting Canada to one point in the first end before an expert double takeout from Grant Hardie freed Mouat up to score two points and give his team a 2-1 lead.
In the third, Canada hit back with two points and then had an opportunity to build their lead with a steal, but a mistake in the fourth by Jacobs left the slightest of openings for Mouat to score a single and tie the game at 3-3.
Another Jacobs miscue meant Canada took just one point in the fifth and a perfect double takeout from Mouat put Britain back into the lead.
The teams traded singles in the next two ends, but with their backs against the wall, it was Canada who dealt the death blow in the ninth end.
A couple of missed shots from Britain allowed Canada to lie four, and Mouat could only make them sacrifice one of those, giving up three points, which Jacobs turned into the win with a steal of one.
The game was decided by incredibly fine margins between the teams' performances, with Canada's shot success percentage of 87% just about trumping Britain's 86%.
Switzerland won the bronze medal after thumping Norway 9-1 on Friday.