The Ashton Gate crowd, who are yet to see their side lose at home under the former Nottingham Forest boss, watched their side carve out plenty of chances against Brighton but they failed to find a way past Tomasz Kuszczak.
Albion, who failed to have a shot on or off target, put in a resolute defensive display to earn a point which keeps them in the play-off places.
In a quiet opening to the match the first save either keeper had to make was Kuszczak's simple stop from Paul Anderson's 25-yard effort in the 18th minute, as City looked to make it five successive home wins.
The home side continued to create all the openings with Liam Kelly's right-footed volley forcing a save out of Kuszczak in the Brighton goal and then Marvin Elliott heading Greg Cunningham's left-footed free-kick over the crossbar.
City, who drew 0-0 at Blackpool on Saturday, were doing their best to avoid a repeat of that scoreline and Marvin Elliott threatened shortly after with a 25-yard shot that bounced wide after he was fed by Anderson.
Next to threaten was Jon Stead, who scored twice in City's last home game, but he headed straight at Kuszczak after being found by Liam Fontaine, another goalscorer in that 5-3 win over Barnsley.
Brighton's defence was holding strong as the match moved into the final 10 minutes, with Anderson unable to test the former Manchester United keeper after Brendan Moloney found the former Liverpool winger.
And for the second game running O'Driscoll introduced Ghana winger Albert Adomah with a few minutes remaining as they looked to make their dominance count.
Jose Ullua showed his talents going forward for Albion on Saturday but he played a part at the other end as the game reached added time, the striker clearing Adomah's right-footed corner out of danger as his side picked up a hard-fought away point.
