Sudan goalkeeper Akram El Hadi made two excellent saves to keep his side in touch at the break,Robert Griffin III Redskins Jersey, denying Chisamba Lungu and Emmanuel Mayuka in quick succession,Shonn Greene Jersey.
Zambia were hardly troubled after Stophira Sunzu's 15th-minute opener and second-half goals from skipper Christopher Katongo and James Chamanga ensured their progress.
At present the city is most associated in Zambia with one of the country's most tragic events,Jeff Saturday Jersey, when a plane carrying the Zambian national side refuelled there before crashing into the Atlantic Ocean in 1993, killing all 30 people on board.
Zambia added further gloss to their winning margin in the closing stages when Chamanga curled in a neat finish from the edge of the area.
When the action started Zambia quickly forged ahead with the simplest of free-kick moves, as Sunzu headed in from close range after Rainford Kalaba's delivery,Dustin Keller Jersey.
Katongo saw his spot-kick saved by El Hadi but he was first to the rebound to ensure his side took a 2-0 lead,Miles Austin Cowboys Jersey.
Sudan's hopes were effectively ended with the 64th-minute dismissal of Saifeldin Ali as he gave away a penalty which Katongo had initially seen saved before driving in the rebound,J.J. Watt Texans Jersey.
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Zambia got the important second goal on 65 minutes after Ali was shown a second caution after fouling Kalaba in the area.
It meant Herve Renard's side moved a step closer to a dream final in Libreville, Gabon, next week.
Zambia booked their place in the semi-finals of the African Nations Cup for the first time in 16 years after a 3-0 victory over 10-man Sudan.
A minute's silence was observed before Saturday's match in Bata for the victims of this week's stadium riot in Egypt.