O'Driscoll proved he is not afraid of making tough decisions when he replaced under-performing keeper Alan Blayney at half-time.
Blayney was put under the microscope throughout the first half but when Pawel Abbott and Mark Hudson did make the breakthrough their finishing was wayward.
O'Driscoll's move looked inspired within minutes of the re-start when Budtz produced a brilliant tip over from Hudson.
Budtz staked his claim for a starting berth with a commanding and aggressive performance in which he took charge of the Rovers defence and looked instantly at home.
Huddersfield strikers Abbott and Andy Booth would have been cursing that they did not cash in on Blayney's hesitancy in the first half.
O'Driscoll also made another sound substitution when he pulled off midfielder Jason Price to save him from a red card.
Price escaped with a first-half booking for an apparent elbow which left Gary Taylor-Fletcher flat out on the pitch and after that he and Town captain Nathan Clarke had a running battle.
The pair clashed again just past the hour-mark and referee Phil Joslin gave him a final warning. O'Driscoll had seen enough and hauled him off.
It was good judgement by the new boss whose side then went on to claim a valuable first point.
Huddersfield's best chance in the first half fell to Abbott who was brilliantly set up by Danny Schofield. Abbott beat Blayney but just as it seemed his shot would creep in at the far post, left-back Gareth Roberts scooped it off the line.
Just before the break Town keeper Matt Glennon blocked a stinging effort from on loan Brian Stock.
In the second half it was all Huddersfield, although Budtz stood firm.
Booth headed over before lightning acceleration from Schofield created a chance for Booth but his clever flick was smothered by the keeper.
Schofield forced Budtz into action once again late on and even though Mr Joslin allowed four minutes of stoppage time for a game littered by petty hold-ups, Huddersfield ran out of ideas and time.