But Declan Devine's side were a wholly different proposition in the second half.
Two corners in quick succession after the restart may not have seemed much, but it marked a considerable uptick in their application of pressure, and their improvement was rewarded by Donnelly's excellent finish from the edge of the box when teed up by Daniel Amos.
Confidence suddenly seemed to course through the visitors, even if Gyollai's save from Ethan McGee was a reminder of the work still to be done at the back.
Indeed, so keen were their players now to have a go, Donnelly and David Fisher attempted to strike the same bouncing ball.
Amos' set-piece deliveries were posing an increasing threat and, when centre-back Frankie Hvid powered one delivery past Chris Johns, the game had been completely turned on its head.
The 19-year-old, who scored the winning goal against Carrick Rangers when Glentoran last won away in the league, wheeled towards the visiting end in Windsor Park with even the celebrating supporters surely having doubted that such a comeback was in the offing.
As if to rub salt in the wounds for Linfield, the icing on the cake for Glentoran came when former Blues midfielder Cameron Palmer picked the pocket of Shields and slid the ball past Johns to make the points safe with ten minutes remaining.
As they wait to see whether they fall from top spot over the remainder of the Irish Premiership weekend, David Healy's side will rue the chances missed in that dominant first half. Glentoran, meanwhile, will hope this memorable derby win can kickstart their season.