Substitute Derk Boerrigter and Kris Commons struck late on in an enthralling Scottish Premiership encounter to leave the Celtic faithful happy ahead of Tuesday night's Champions League visit of Milan.
Commons opened the scoring in the 35th minute before former Hoops forward Niall McGinn levelled in first-half added time.
In an entertaining second half, Georgios Samaras hit the woodwork and McGinn had a shot tipped onto the post by Celtic goalkeeper Fraser Forster with three minutes remaining.
But, in the first of three added minutes, Boerrigter - on for Teemu Pukki - prodded the ball over the line from close range for his first goal for the champions before Commons grabbed his second to seal the outcome.
The Hoops boss said the late-late show evoked memories of his time as a Celtic player. "You need patience at times," he said. "It is not always going to be free flowing football.
"I know from my own days under Martin (O'Neill) and Gordon (Strachan) that you get games like that.
"There is many a time we won in the last minute of games at home and this team has the same ingredients and I am delighted with that.
"Teams come here and be hard to break down and the onus is on us to find a way to break them down and we are doing it.
"The character of the team is fantastic. The quality could be better but it will be better as the season goes on.
"We are unbeaten in 13 (league) games which is a brilliant start to the season so I have no criticism of the team at all."
The Northern Irishman expects to have James Forrest back from a hamstring injury and Anthony Stokes back after personal issues led to him missing the Dons game for the midweek visit of the Italians.
He said: "Psychologically, today it gives us a massive lift. We won our home game against Ajax and played very well in the San Siro.
"Milan will be different, they have a couple of players back so all the ingredients are there."
Boerrigter's Celtic career has been hampered by an ankle injury he brought with him when he signed from Ajax in the summer but after scoring his first goal for the Hoops he is hoping to face the Rossoneri.
"I am very delighted now and can't wait to get more goals," he said. "But my first priority is to get fit again, to be at the level that I used to
play and hopefully I can get more minutes.
"I am not entirely over my ankle injury but we are working hard to get there.
"It has been a long time. Before I came here I had the injury and I got a lot of kicks on it here.
"I got time off to recover and that helped and I am feeling better now."
Dons boss Derek McInnes claimed it was Celtic's "determination" that made the difference.
He said: "It wasn't quality that beat us and I mean that with all due respect to Celtic.
"They have loads of quality players and they are here because they are winners and more determined, more than anything.
"It was their determination to get the ball over the line which ended up beating us."