With the sides goalless after extra time Zambia's Stoppila Sunzu converted the magic spot kick after Arsenal striker Gervinho missed for the Elephants.
The result meant misery for the star-studded Ivory Coast, who failed to claim the title despite not conceding a goal throughout the entire competition until Sunday's final.
The match was staged in Gabonese capital Libreville, off whose coast a military aircraft carrying the 1993 Zambian national squad plunged into the Atlantic Ocean killing all 30 players, officials and crew on board.
Zambia coach Herve Renard commented: "This represents something enormous, something which appeared unrealisable before the competition began.
"I know we're not the best but we have a strength and force that animated our team."
Former Cameroon International and National Soccer League player Cyrille Ndongo-Keller said: "Football in Africa is more than what you see on the field. It captures the social and political.
"It's good to see Zambia, with just over 10 million people, go home with the Cup."
Zambia covered themselves with glory, hassling and harrowing their way to the penalty lottery, and then holding their nerve to prevail in the dramatic, barely watchable denouement.
Ivory Coast coach Francois Zahoui said: "We didn't expect such challenging a final.
"This is a big disappointment for us. We didn't have much luck, we missed the penalty in normal time, then perhaps lost a bit of confidence.
"We go back to Abidjan with not too much shame. I think we've played a good game. I congratulate Zambia."
Zahoui fielded the same side that saw off Mali 1-0 in the semi-final.
Renard recalled striker Emmanuel Mayuka, after his starring role in getting the decisive goal in the 1-0 last four defeat over Ghana.
He joined captain Christopher Katongo in spearheading the Chipolopolo's (Copper Bullets) attack.
A minute of silence was observed before kick-off in memory of the 74 people killed in the Port Said stadium slaughter in Egypt.
The game was only seconds old when Zambia almost took a shock lead, with keeper Boubacar Barry doing well to save Nathan Sinkala's close range shot off Katongo's quick pass from a Rainford Kalaba corner.
Renard was forced into an unscripted change when defender Joseph Musonda limped off in tears on 11 minutes - Nyambe Mulenga took his place.
A shaky start by Ivory Coast gave Zambia hope of an upset and Kalaba's 30m free kick wasn't far off finding the back of the net after taking a deflection off Cheik Tiote's leg.
The Elephants put together their best passage of play approaching the half hour mark - a neat Drogba backheel setting up Yaya Toure only for the Manchester City midfielder's angled shot to go wide of the far post.
A hugely promising first half from Zambia had the Elephants' defence, marshalled by Kolo Toure, under more pressure than they would have wanted, with Katongo leading from the front.
Zahoui, ressembling a New York policeman with black trenchcoat and baseball cap, walked into the dressing rooms at half-time with a face like thunder.
The second half began with a deathly hush descending on the stadium - the final in desperate need of the kiss of life in the guise of a goal.
And on 72 minutes one should have come after Ivory Coast were awarded a penalty when Issac Chansa and Mulenga barged into Gervinho.
Drogba stepped up but his woeful attempt went soaring into the night sky, even though he appeared to divert blame to the pitch, glaring at the spot.
This was his second miss from the spot after he had a penalty saved in the quarter-final win over Equatorial Guinea.
In the 95th minute, substitute Felix Katongo crossed from the right for his brother Christopher with only Barry's toe diverting the goalbound ball off the near post.
There was electric tension once the penalty shoot-out got underway, with Kolo Toure missing the Ivorians seventh spot kick, but Zambia's Kalaba also missing his to leave the sides still inseparable.
Then after Gervinho failed in his attempt it was left to Sunzu, the defender who plays his club football in the Democratic Republic of Congo, to give Zambia a historic first title, and consign Ivory Coast to another wretched defeat.
French coach Herve Renard and a squad containing only one player who lines up for a first division club in Europe vowed to bring the trophy back to Lusaka as a tribute to those who died in 1993.
Ndongo-Keller summed up Zambia's performance: "To come in and hold your own and push Ivory Coast to extra time and actually win the game, as they say in Africa, it's destiny."
