A quiet opening half of football came to life when James Meredith opened the scoring for the Bantams after 36 minutes.
Bradford began the second period as they ended the first, their pressure paying off immediately as Cole's pace saw him get in behind United's defence.
On-loan Birmingham defender David Edgar, in his attempts to clear the danger, kicked the ball off the on-rushing Cole leaving Howard no chance as City went 2-0 up.
Bradford were pinned back for most of the second period but almost went ahead through Anderson, whose header from close range was straight at Howard.
The Bantams came closest to winning the tie in the end, Baxter clearing James Hanson's header from Knott's corner off the line.
The derby draw means that the Blades move up to 7th position in League One while Bradford occupy 12th place.