First team squad members Cammy Smith and Craig Storie started in place of Seb Ross and Aaron Norris while Sam Robertson was replaced at right back by Paul Lawrie Foundation graduate Joe MacPherson.
Celtic showed plenty of attacking intent in the opening quarter of an hour, forcing three corners but Aberdeen defended well and Lennox didn?t have a direct save to make.
Good interplay between Thomas and Wright created an opening for the Welshman but his 18 yard shot flew over the bar.
Miller on the left for Celtic was causing problems but his deep cross found nobody in a hooped shirt in the middle. Aberdeen had a set piece opportunity but McKenna headed wide from Thomas? well flighted delivery from the left.
Celtic looked dangerous going forward and Archibald?s deep cross from the right found Miller but the wide man headed meekly wide when he really should have tested Aaron Lennox.
The Sydney born stopper came to the home side?s rescue on 34 minutes producing a brilliant point blank save to palm away Thomson?s header after a corner.
Aberdeen were fighting it difficult to create any clear cut openings but Scott Wright and Cammy Smith always looked a threat, the latter firing wide just before the interval.
Celtic brought on Higgins in place of Lafferty at the start of the second half.
The visitors almost broke the deadlock on 48 minutes when an acrobatic effort from Archibald crashed off the bar with Lennox beaten. Celtic were piling on the pressure but Scott McKenna was marshalling his defence well.
Aberdeen introduced Sam Robertson to the fray just before the hour mark as he took over from Joe MacPherson at right back.
Despite incessant Celtic pressure it was the Dons who scored the opening goal on 65 minutes and it was a beauty. Lewis Hutcheson cut in from the left and played a wonderful ball inside the full back for the overlapping Sam Robertson whose perfect cross was bulleted into the net by the head of Joe Nuttall. A superb goal.
Cammy Smith and goalkeeper Aaron Lennox were withdrawn from the action as Seb Ross and David Craddock took over. Celtic?s Thomson became the game?s first booking after a foul on Wright.
Celtic drew level on 81 minutes when Sam Wardrop powered a close range header past Craddock following a Thomson corner from the right. The quality of the delivery meant the visitors were always a threat from set-pieces but up until that point the Dons had defended very well.
The last ten minutes or so were end to end.
Craddock, who made a couple of good saves whilst on the pitch, blocked well from Miller then Harvie hit a fierce drive just over as both sides went for a winner but it wasn?t to be. McCart was booked for dissent.
Celtic were delighted to keep their unbeaten record intact but the Dons made them fight all the way and richly deserved their point.