The Bantams' Congolese star was dismissed two minutes before the break for a second bookable offence, but Bradford boss Stuart McCall was fuming about full-back Laurence Wilson's theatrics which looked to have conned referee Graham Salisbury.
Bradford were already leading thanks Peter Thorne's first goal since January 2006, but they had to defend for their cup lives as Chester pressed forward for most of the second half.
Despite being a man down Bradford keeper Donovan Ricketts, who had made two excellent first-half saves, was hardly tested thanks to some backs-to-the-wall defending.
Ricketts did well again to keep out a low drive from Chester midfielder Mark Hughes when he burst into the Bradford box after 56 minutes, but the Bantams hung on to bag a second victory over their League Two rivals in the space of five days.
The game burst into life after 19 minutes when Ricketts, who had saved a penalty in Tuesday's 2-1 league win, dived to his right to push away a Hughes volley.
Two minutes later Bradford midfielder Eddie Johnson wasted a superb opening when he guided his four-yard shot wide of the goal, after being picked out by Paul Evans' pin-point free-kick.
But Thorne made sure the miss wasn't too costly when he rose superbly to meet another excellent Evans cross and power his 14-yard header over the stranded John Danby.
The injury-plagued striker last scored for Norwich almost two years ago and his 27th minute finish was a timely reminder of his ability.
Ricketts made another good block to keep out a Tony Grant header on the half hour mark, but Bradford's hopes suffered a setback when Ndumbu-Nsungu was giving his marching orders.
The striker had already been booked for a needless kick on Wilson and when the Chester man went down in front of the dug-outs, referee Salisbury harshly reached for his card again.
Bradford were content to soak up the pressure after the interval and they even threatened a couple of times on the break, but Chester will rue the fact that they failed to make the most of their extra man.