Kelly averaged 57.345 kph to beat Soren Lausgberg of Germany by eighteen hundredths of a second. The bronze medal went to another German, Jan Van Eijden, in 1:04.541.
Local hero Boardman took over two seconds off the record he established in Wednesday's first round as he destroyed Italy's Olympic champion Andrea Collinelli in the final.
Boardman clocked an amazing 4:11.114 seconds as he beat the former world record-holder by the massive margin of over nine seconds.
The Italian who inherited the Olympic crown in Atlanta which Boardman did not defend simply had no answer to the power of his rival.
Both men were using the arms fully outstretched "Superman" style invented by former British world champion Graeme Obree that Boardman only adopted in training last week.
The 28-year-old, who sliced six seconds off Collinelli's world record on Wednesday, extended Britain's winning run in the pursuit to four years as he regained the title he won in 1994 in Sicily. Obree had won on the two other occasions.
As in his three previous rounds, Boardman gave the advantage to his opponent in the early stages as he fully cranked up to the higher gear he uses.
The Italian built up a lead of over one-and-a-half seconds by the time they reached the 1500 metre point and was still hanging on as they went through the midway point in world record-breaking time.
But the advantage soon came tumbling down and in the space of a few laps Boardman had built up a title-winning lead to the delight of the 3,000 sell-out crowd at the home of British cycling.
They were able to cheer him on to the new world record as he easily smashed the time of 4:13.353 he set on Wednesday.
In his four races over the past two days Boardman has clocked the four fastest times in history.
He has taken the pursuit event onto a higher plain that will test even the powers of Obree who missed these championships because he is still feeling the effect of the viral problems that wrecked his Olympic challenge.
Boardman's next goal will be to return to Manchester a week from Friday where the coveted world hour record -- cycling's blue ribbon event -- should surely fall to him once again.
Frenchman Francis Moreau, his GAN team-mate, took the bronze medal after clocking the fastest time of the two beaten semi-finalists.
Boardman had easily disposed of teenage Russian Alexei Markov in his semi two hours before the final when he won by eight seconds in a time of 4:15.006.