The contest was played throughout at a high tempo with chances to both sides in the tenth minute.
First Notts' debutant goalkeeper Russell Hoult saved smartly to deny Eddie Johnson before County broke away only for Jay Smith to send a volley skimming just past goalkeeper Scott Loach's left-hand post.
Bradford had the best chance of the half in the 25th minute when Willy Topp broke clear before lifting his effort over the bar, Hoult deserving credit for coming out and narrowing the angle.
Notts stormed at Bradford at the beginning of the second half and Loach made an unorthodox save, punching away another effort by the lively Smith.
The lead Notts were threatening to take arrived in the 58th minute. Richard Butcher had a shot blocked and the ball broke invitingly for Ryan Jarvis to pick his spot and score for Notts for the first time during his loan spell from Norwich City.
Within five minutes, however, Bradford were back on terms when Peter Thorne side-stepped his way past central defender Adam Tann and found the net with a thumping finish.
Then, on 69 minutes, Ali Gibb was responsible for giving the ball away to Joe Colbeck who rifled his effort past Hoult.
Bradford tied up the points with a third goal 15 minutes from time. There was a lovely inter-passing move between Omar Daley and substitute Alex Rhodes which the latter finished with a lovely angled drive beyond Hoult.
There was still more work for both goalkeepers to do. After Hoult had denied Thorne, with City looking for a fourth goal, Loach pulled off even better work at the other end with a double stop from substitute Spencer Weir-Daley and Paul Mayo.
But in the end Notts' defensive lapses had cost them dearly as they plunged to a ninth home defeat of the season.