The Gunners have now won nine of their last ten outings at the home of Scottish rugby in all competitions since last Christmas.
The defeat means Glasgow, whose squad had been struck down by a mystery throat and stomach virus ahead of the game, have won just one of their past seven matches in all competitions.
And to add to their woes, Calvin Howarth was stretchered off in the dying seconds with a suspected broken leg.
The victory also continued Edinburgh’s dominance over their local rivals at home, where they have not lost since a 24-25 reversal in the Scottish Inter-District Championship at Pennypit Park, Prestonpans in 2001.
Edinburgh opened the scoring with a long range penalty from Chris Paterson but Glasgow rallied with the opening try of the game from hooker Scotty Lawson however Dan Parks could not add the extras.
Paterson narrowed the deficit shortly after with his second penalty of the game and a drop goal followed to give his side the lead.
Veteran Scotland lock Scott Murray then crossed for the home side’s first try and Paterson’s conversion extended their lead to 11 points.
Glasgow’s finishing let them down late in the half and they were made to pay when the Gunners grabbed their second try before the break.
A sloppy turnover allowed scrum-half Rory Lawson to race away to score from inside his own half.
Paterson was once again in target to put his side in complete control.
The visitors rallied late on with their second try through Andy Craig, which was converted by Dan Parks but their hope was soon extinguished when centre Rob Dewey benefitted from some good work by Ali Hogg to score his side’s third try.
The closing moments of the game were over-shadowed by the injury to Howarth who was taken immediately to hospital.