Zanzala's brace, alongside a header from defender Rhys Bennett, meant that Gareth Evans second half strike was meaningless as the Cumbrians clinched their first victory in eight, putting a stop to the rapid decline of the club.
This result meant Carlisle had completed the double against their Yorkshire counterparts, with Bennett scoring in both ties.
Carlisle United: Farman; Tanner, Bennett, MacDonald, Armer, Riley, Guy, Mellish, Zanzala, Alessandra, Dickenson
Bradford City: Hornby; A O'Connor, P O'Connor, Canavan, Wood, Watt, Sutton, Vernam, Evans, Crankshaw, Cook
Story of the match
Evans had an early chance to send the Bantams into the lead as he pounced onto a cross from Charles Vernam, but he hesitated before the Carlisle defence rushed back and turned him away from goal.
Carlisle responded almost immediately, as a long throw-in from Brennan Dickenson was cleared out to former Bantam Callum Guy, whose volley was acrobatically kept out by Sam Hornby.
However, questions were raised as Carlisle missed a golden opportunity to take the lead. Dickenson opened up his body on the edge of the box, before unleashing a strike that was excellently saved by Hornby. The ball fell to Lewis Alessandra, but he scuffed his rebound into the empty net, and Paudie O'Connor heroically cleared off of the line.
But Carlisle's pressure was finally rewarded. A whipped cross from the corner confused the Bradford defence, and Bennett managed to find himself unmarked six yards out, allowing him to head the ball into the ground and past a helpless Hornby to grant the Cumbrians the lead.
And within the space of three minutes, the lead was doubled courtesy of Zanzala. Another corner caused some further poor defending from the Bantams defence, as a huge goalmouth scramble allowed Zanzala to bundle the ball over the line. The linesman flagged for a foul on Hornby, but the referee waved away his claims and awarded a deserved goal for Carlisle.
Heading into the second half, Trueman and Sellars' made the change of bringing on Danny Rowe for Crankshaw, with the hopes of finding a route back into the tie.
But Carlisle nearly got their third, as George Tanner burst past his man and shot at Hornby, but he spilled the save and Paudie O'Connor was once again present to scramble the ball clear from the line.
Joe Riley took aim from 25 yards, but Hornby was there to smother his audacious strike.
Bradford simply weren't at the races, as Carlisle snatched their third and Zanzala's second. Dickenson once again created a chance, as he floated a deep cross onto the head of the Congolese striker, who nodded past Hornby before reeling away in jubilance.
The Bantams did spark hopes of a potential fightback in the 63rd minute, as a deep cross was nodded back into play by Niall Canavan into the path of Evans, whose volley was deflected into the back of the net.
Evans tried to spawn a brace, as he raced onto a Billy Clarke ball but Evans strike was thwarted by the legs of Farman.
Minutes later and another chance for Bradford, as Rowe nodded Cook through on goal, but as he squared down the goalkeeper he scuffed his chipped effort and it bobbled narrowly wide.
Zanzala missed a crucial chance to nick his hattrick, as he found himself unmarked at the back post but could only head into the side netting.
As the clock ran down and Bradford squandered a few opportunities, the full-time whistle was blown. Carlisle recorded their first double over the Bantams since the second world war.
In what could only be described as the perfect time to play Carlisle, Bradford crumbled and continued the slight blip that they have taken under Trueman and Sellars.
Their third defeat in their last 17 games, the Bantams have failed to pick up a win in their last three and mustered just two shots on target. The City defence looked disorganised and lacked communication, with the usual back four certainly having an off day.
Carlisle will be delighted to have finally escaped their abysmal form, and will now hope to climb back up the table.
They'll also be pleased with Zanzala, who has struggled to score this season so this could be the confidence boost to get him firing.
Starman - Offrande Zanzala
Plaudits have to go to Zanzala for his dominant display up top, bullying one of the most strong defences in the league and causing a constant headache for the Bradford defence.