Birmingham twice took the lead, with Remeao Hutton and Kyle McFarlane scoring either side of Walker's first goal to put the Blues 2-1 ahead.
But Alex Cover put the Rams on level terms almost instantly before Walker's penalty gave the hosts a 3-2 half-time advantage.
Walker (pictured above) completed his hat-trick five minutes after half-time. Ikechi Anya then scored twice before setting up Walker for his fourth and Derby's seventh.
Derby have nine points, three more than second-placed Nottingham Forest and six ahead of Middlesbrough and Birmingham.
Derby: 28 Jan v Liverpool (A) PL2
Birmingham: 5 Feb v Forest (A) PL Cup