City were held to a frustrating draw by npower Championship strugglers Millwall at Ashton Gate.
Steven Davies' spectacular long-range header gave City the lead on 28 minutes, but familiar suspect Darius Henderson levelled things up seven minutes before the break.
It seemed certain on the pattern of play that there would be further goals after the interval, but Adomah and Davies squandered the best of them and City had to settle for a solitary point.
In truth Millwall finished the stronger, and may well have snatched an unlikely victory at the death.
Derek McInnes made five changes to his side condemned to back-to-back home defeats by Leeds United on Saturday.
Steven Davies was handed his first City start, Lewin Nyatanga his first of the season and Cole Skuse his first since being stretchered off at Peterborough a fortnight ago.
Also returning were Mark Wilson and Sam Baldock, as McInnes fielded another attacking line-up with his intentions to continue the recent Ashton Gate goalrush evident.
It nearly paid early dividends, as Baldock raced away down the right and aimed a low cross towards the penalty spot.
When Millwall failed to clear, the ball fell invitingly for Stephen Pearson 18 yard out in a central position, but the Scot just dragged his shot inches wide of David Forde's left-hand post with the keeper rooted to the spot.
City should have been 1-0 up, but were soon relieved to see Darius Henderson pass up a glorious opportunity to open the scoring at the other end.
Running clear in behind the Robins' wide open defence, the striker could only shoot wide of the near post as the ball nestled on the wrong side of the net for the visitors' liking via the hoardings behind Tom Heaton's goal.
Davies was keen to make an impression, threatening a deadlock breaker four times before doing so on 28 minutes. First, a swirling free kick narrowly eluded the far post, before he drove two speculative shots off target from distance.
But it was clear his confidence was there, and an extraordinary opener would have done nothing to dampen his growing self-belief.
Skuse's high ball over the top was designed for Baldock to chase, but when Forde vacated his line to deal with the danger, he was forced to use his head to clear the ball from the edge of his own penalty area.
It still seemed likely to suffice when the ball dropped towards Davies 30 yards from goal, but an extraordinary header back over the keeper's head bounced once and found the roof of the net for a most unusual opener.
City were playing with real pace and a sharpness that was keeping Millwall on the back foot, but with no clean sheet this season a single goal was always unlikely to be enough.
Sure enough, seven minutes before the interval it was 1-1, as regular City scourge Henderson gleefully exploited the space afforded to him inside the penalty with a powerful header past Heaton from Alan Dunne's pinpoint cross.
It had been a lively first half, and former Ashton Gate loanee Chris Wood threatened to have the final say from a glorious chance on the stroke of stoppage time, but headed straight at Heaton from a position demanding better.
With City attacking the East End in the second half, Albert Adomah had a gilt-edged chance of his own from virtually the same spot as Wood, but somehow contrived to clear the crossbar on his left foot for a glaring miss.
Meanwhile, Davies continued to rack up the attempts at goal as another free kick whistled past the post, before he spurned a wonderful opportunity to double his tally for the night when fed by Skuse, lashing the ball high into the side netting as Forde raced off his line to meet him.
City continued to press, but the succession of chances created in the first hour petered out. McInnes introduced Brett Pitman for the first time since the opening game of the season at Nottingham Forest, but his team were unable to carve out a decisive opening.
In the end it was Millwall substitute Andy Keogh, once of City, who came close to a winner, but his glancing header drifted narrowly wide before Henderson shot wide in injury time, as both teams shared the spoils.