A 15th minute goal from defender Stopilla Sunzu, a second after 66 minutes from captain Chris Katongo and a third four minutes from time by James Chamanga ensured Zambia reached their first Nations Cup semi-final since 1996.
Sunzu rose unchallenged to head home a free-kick as Zambia stamped their dominance on the match almost from the start in a workmanlike performance.
Katongo scored on the rebound after his penalty attempt had been saved by Sudan's Akram El Hadi Salem for his third goal of the tournament.
The penalty came after tricky play down the wing forced a trip on Rainford Kalaba by Saifeldin Ali Hidris, who got a second caution to became the fifth player sent off at the tournament being co-hosted by Equatorial Guinea and Gabon.
Substitute Chamanga curled home a shot from inside the area in the 86th minute to complete an easy win for Zambia after some sloppy defending by Sudan.
EARLY EFFORTS
Zambia had two early efforts to signal their attacking intent before the opening goal while Sudan sought to break on the counter and were restricted to shooting from distance.
"Sudan can make you go to sleep with the way they play but we were expecting it," said Zambia coach Herve Renard. "We know Sudan well from regional tournaments and so we sought to take charge straightaway.
"We hope now to go all the way to the final on the 12th. Ghana are the big favourites now in my opinion but they are a team we'll be prepared for if they win through. Tunisia are a formidable team too," added Renard.
Sudan had reached the last eight for the first time since 1970 but rarely troubled the Zambian goal.
"We achieved our objectives and we consider this a success, even though we lost today," said Sudan coach Mohamed Abdallah. "We gained experience and ambition."
