It is the first time since 1989 that the same rider has won both prestigious and difficult shows in the same year.
At the same time, Paget has entered the running to win the eventing Grand Slam, with a CCI4* in Lexington still to come next spring.
However, the HSBC FEI Classics 2012-2013 still belongs to his compatriot and world number one Andrew Nicholson, who placed second with Avebery, third with Nereo and eight with Calico Joe in Burghley.
Nicholson's consistency was rewarded with a cheque for $150,000.
New Zealand dominated proceedings at Burghley, with six of the top 10 positions occupied by Kiwis. Along with Paget and Nicholson's placings, Jonelle Richards came in sixth and Mark Todd seventh.
Britain's William Fox-Pitt broke up the Kiwi dominance by coming fourth with Parklane Hawk, ahead of Germany's multiple European medallist Ingrid Klimke with FRH Butts Abraxxas.