The cyclist is the first UK Olympic athlete to achieve the feat since swimmer Henry Taylor at the London Games in 1908.
Team mate Bradley Wiggins was earlier unable to complete a hat trick of golds, coming eighth in the Madison with partner Mark Cavendish.
He had a gruelling Olympic schedule and had already won gold for the individual and team pursuit.
Miner's son Taylor won the 1,500 metres, 400 metres and was part of the victorious 4 x 200 metres relay team.
He was Britain's greatest ever Olympic swimmer, achieving another bronze in 1912 and again in 1920.
The athlete also won three medals – bronze, silver and gold – at the unofficial Olympics in Athens in 1906, which was held to mark the tenth anniversary of the first modern Games.