The 1872 Cup is awarded to the aggregate winners of the derby double-header, and the Warriors won the first contest 23-14 at Scotstoun following a fast start - before repeating the first-half onslaught in the capital.
Glasgow had nine fingers on the trophy and the RaboDirect PRO12 points almost sewn up after 40 minutes, taking a 16-3 lead courtesy of tries from New Zealand-born, Scottish-qualified wing Sean Maitland and Ruaridh Jackson, plus two penalties from Peter Horne, who was also sin-binned.
A Greig Laidlaw penalty was the solitary reply for Edinburgh, who last won the 1872 Cup in 2008-09, and their hopes were hit further when Allan Jacobsen was sin-binned and Henry Pyrgos scored a try.
Roddy Grant's converted score after 59 minutes gave the hosts some hope and Tim Visser scored five minutes from time, with Laidlaw kicking his side within four points.
But the late rally ended there as Glasgow saw out the remaining seconds to retain the bragging rights they have held since the 2009-10 season.