Chris Dean's last-gasp try settled matters as Edinburgh edged Glasgow 18-17 in the first game of this season's 1872 Cup, ending the Warriors' 10-game winning streak in the Guinness PRO14 this term.
The result came despite the hosts losing prop Simon Berghan to a red card in the sixth minute.
Glasgow had led 17-6, with Huw Jones (two) and Scott Cummings (57) scoring tries, the first converted by Peter Horne and the second by Finn Russell. But Edinburgh replacement scrum-half Nathan Fowles kick-started the comeback with a try just after the hour mark, converted by Jaco van der Walt, before Dean's 79th-minute score completed the comeback. Sam Hidalgo-Clyne also kicked two penalties for the hosts.
The three-game series continues at Scotstoun next weekend. Saturday's match got off to the perfect start for the visitors, with the opening try after just two minutes. Wing Tommy Seymour appeared as centre-field receiver and fed centre Jones, who touched down for Horne to convert.
Stung into action, Edinburgh immediately went up field and were initially awarded a kickable penalty by referee Frank Murphy.
However, TV evidence showed Berghan's foot had made contact with Glasgow hooker Fraser Brown's head in the preceding ruck, and Murphy produced the red card to reduce the hosts to 14 men.
Edinburgh did manage to pull back three points with a penalty from scrum-half Hidalgo-Clyne on 18 minutes, but struggled to make further inroads.
Glasgow looked poised to extend their lead five minutes before the interval, but twice Edinburgh held the ball up over their line.
Horne and Hidalgo-Clyne exchanged penalties within 11 minutes of the restart to maintain the status quo.
Russell was introduced from the replacements' bench on 50 minutes, and Glasgow swiftly scored a second try, from a driven lineout. Lock Cummings touched down, with Russell adding the extras.
Edinburgh hit back with Fowles finishing off a lineout drive in the 61st minute, with Van der Walt converting, and the hosts' spirited push for victory in the final 10 minutes were rewarded with the decisive late try from Dean.