Striker Dave Hibbert had the honour of scoring the first ever league goal at Town's new home – his ninth minute penalty securing a victory the Shrews' just about deserved.
This was a hard-fought victory for Gary Peter's men, as Town had to withstand several long spells of Bradford pressure, with a superb save from keeper Glyn Garner at the death ultimately securing the points.
In the fourth minute winger Marc Pugh skipped past City full-back Darren Williams to flash a shot across goal.
Soon after, there was no such escape for the visitors as Pugh once again showed Williams a clean pair of heels, only to be brought by the despairing defender.
From the ensuing penalty Hibbert, who had a long-spell on-loan at Bradford last year, stepped forward to send City keeper Donovan Ricketts the wrong way and give Shrewsbury the lead.
On 19 minutes Pugh again tormented the Bradford defence with his centre headed firmly against an upright by Hibbert.
As the half unfolded City came back into the contest and only a smart save from Garner prevented them from drawing level, plunging to his left to hold Paul Heckingbottom's curling free-kick.
After the break Bradford continued to push for a leveller, but at the other end Ricketts saved well from Shrewsbury centre-back and man of the match Kelvin Langmead when he met Pugh's corner with a fierce header.
As the game came to a conclusion, City went all out for an equaliser – which former Shrewsbury man Paul Evans looked to have secured them right on the final whistle, only to see his fizzing drive turned over the bar by Garner in breathtaking fashion.