Just how damaging a week this has been for Celtic remains to be seen, but for the second successive weekend they shed points in the Scottish title race - in this instance in injury-time of a compelling contest which yielded six goals, three from penalty kicks, of which two were converted by Lewis Ferguson of Aberdeen.
The champions had to come from behind twice and despite dominating the first half they conceded the opener to Ferguson's first conversion two minutes before the break after Olivier Ntcham had fouled the Dons' midfielder.
After the interval, Celtic drew level through Callum McGregor, fell behind again to a Ryan Hedges strike, equalised from a Ryan Christie penalty and took the lead through Leigh Griffiths only to concede again to a last-ditch Ferguson spot-kick.
It was a sore end to a passage that began with defeat at home to Rangers and continued with a 3-1 Europa League loss to AC Milan at Parkhead on Thursday.
Even by Pittodrie standards, conditions at kick-off were punitive, with rain driven into the players' faces. The experience was nevertheless welcome for Scott Bain, making his first start since playing in the opening weekend victory at Hamilton.
He replaced the rested Vasilis Barkas, while Scott Brown was on the bench along with Stephen Welsh, who had also started the previous two games.
The signs were that the game would reach its midway point without goals until Ntcham was drawn into what Willie Collum construed as a mis-timed challenge on Ferguson - who then beat Bain from the spot with Aberdeen's first shot on target.
Neil Lennon had spoken beforehand about his players' character and it was evident when Celtic equalised seven minutes into the second half. From a throw-in, McGregor took a return pass from Tom Rogic and slid his finish beyond Joe Lewis.
Celtic, though, have been vulnerable at the back and Shane Duffy, a repeat offender, inflicted more self-harm when he drove an attempted clearance off Scott Wright into the path of Sam Cosgrove, whose shot was parried by Bain. The rebound fell to Hedges, who forced his shot home.
Lennon responded by replacing Ntcham and Albian Ajeti with Brown and Griffiths, who soon repaid his manager's faith by sidestepping Ash Taylor to curl a left-foot shot over Lewis. With 12 minutes remaining Celtic took the lead for the first time when Tommie Hoban fouled Mohamed Elyounoussi for yet another penalty kick, from which Christie sent Lewis the wrong way.
Celtic, however, could not see the game out and when McGregor fouled Connor McLennan in stoppage time it was yet another penalty, although the referee played advantage, from which Cosgrove hit the crossbar before the kick was awarded and Ferguson made it 3-3.
"I'm disappointed we haven't won. We showed character to come back twice and we then lose that late goal. Defensively, we were poor but attacking it was good, particularly in the second half," Lennon said.
"There's a little bit of fragility there at the minute and when you score three goals away from home you should win."