The result ended County’s unbeaten away record, the only one in the four divisions.
Parkinson, who praised the physical strength and mental toughness of his players, said: “We wanted to go to Millwall with our own run intact and in a strong position in the League – three points clear in fifth place. We can go there and express ourselves and be confident after two wins over Christmas.”
Midfielder Billy Knott scored the decisive goal after 41 minutes following a mix-up on the edge of the penalty area between keeper Roy Carroll and former Bantams winger Garry Thompson. Andy Halliday picked up the loose ball and cut it back to the unmarked Knott, whose left-foot shot went in off the boot of Hayden Mullins.
Earlier, Halliday was twice off target when well placed while Knott saw his left-foot shot on the turn fly just over crossbar.
Notts’ best first-half effort came in the 22nd minute when Jake Cassidy’s shot from the edge of the area struck the post. Bradford, who lost defender Andrew Davies with a hamstring injury, continued to dominate in the second half. Carroll did well to save from James Hanson and substitute Francois Zoko was inches away from a goal in stoppage time.
Bradford City: Pickford, Darby, Davies (Sheehan 13), McArdle, Meredith, Morais, Liddle, Knott (Kennedy 83), Halliday, Stead (Zoko 79), Hanson. Unused substitutes: Williams (gk), Routis, McBurnie, Mottley-Henry.
Notts County: Carroll, Dumbuya, Adams, Smith (Whitehouse 67), Mullins, Hollis, G Thompson (Murray 85), Cassidy, Jones, McLaughlin, Hall (Bishop 45). Unused substitutes: Pilkington (gk), Traore, Edwards, C Thompson.
Referee: D Bond (Lancashire).
Man of the match: Gary Liddle.