Leeds had seemed on course for their first win of the campaign after taking a two-goal lead inside 52 minutes through Mirco Antenucci and Chris Wood.
But City equalised through substitute Kieran Agard in the 89th-minute before Aden Flint capped a grandstand finish when he bundled home deep into stoppage time after goalkeeper Marco Silvestri had failed to hold Marlon Pack’s header.
City played some decent football at times but were again let down by their shyness in front of goal and it is easy to see why they are willing to break their transfer record with the purchase of Brentford striker Andre Gray for around £9million.
Robins manager Steve Cotterill cut a frustrated figure as his side were denied by a combination of faulty finishing and good goalkeeping from the Italian Silvestri.
It looked as if they would be punished for a third straight league game after Antenucci had profited from a slick Leeds counter-attack six minutes before the break.
Wood slipped in Antenucci and the Italian fell over Ben Hamer’s outstretched arm as the City goalkeeper came rushing out.
Hamer was booked for his part in the incident and Antenucci composed himself to send the goalkeeper the wrong way from the spot for his second goal of the season.
At 1-0 down, Jonathan Kodjia wasted a great chance to equalise after Silvestri could only parry Aaron Wilbraham’s effort and it was a miss that would come to haunt City within seven minutes of the re-start.
Leeds launched another swift raid and this time Antenucci turned provider for Wood to score a first Leeds goal since his summer move from Leicester as he rifled a powerful shot past his former Foxes team-mate Hamer.
City fans were angry the game had been allowed to continue with Wilbraham down injured and their mood was not brightened by the sight of Bamba being booked for the original challenge after the goal celebrations had died down.
The Robins had started in positive fashion as they sought to get the weekend’s 4-2 home defeat to Brentford out of their system.
Wilbraham was foiled by Bamba’s brave defending at the near post and Callum Robinson fired over as the Leeds goal came under mounting pressure.
But Leeds slowly edged their way into the contest and Wood saw his effort deflected wide before Tom Adeyemi headed over Kalvin Phillips’ cross.
Flint rose superbly to power a header goalwards and Leeds were only spared by Stuart Dallas’ sentry duty on the post, but the Robins centre-back would have the final word.