The hosts eventually broke the deadlock on 17 minutes through McGregor, who connected with Kieran Tierney's deflected cross and lashed an effort into the bottom corner.
Although the Hoops continued to push forward in search of a second, AEK remained dangerous on the counter and duly levelled proceedings just before the break.
Celtic's backline failed to deal with a cross drilled across their box, which allowed Viktor Klonaridis to take a touch in plenty of time and strike beyond Gordon in the Bhoys' net.
AEK shot themselves in the foot after the restart, with Galanopoulos sent off after earning two yellow cards in just seven second-half minutes.
Despite having a man advantage, however, Brendan Rodgers's side could not make the most of the opportunity to find a winner as the spoils were shared come full time.
The second leg takes place at the Athens Olympic Stadium on Tuesday, with the winners of the tie facing either Swedish side Malmo or Hungarian outfit MOL Vidi in the playoff round.
CELTIC (4-1-4-1): Gordon; Lustig (Sinclair 77'), Hendry, Ajer, Tierney; Brown; Forrest, McGregor, Ntcham, Rogic (Griffiths 63'); Edouard
AEK ATHENS (4-2-3-1): Barkas; Bakakis, Oikonomou, Lampropoulos, Lopes; Galanopoulos, Simoes; Bakasetas (Saldanha 66'), Victor (Galo 80'), Hult; Livaja (Ponce 77')