Stoppila Sunzu converted the winning penalty after three successive efforts had been missed in a long and nervy shootout that totalled 18 kicks.
But the goalless match might not have had to go to the shootout had Drogba not ballooned a 70th-minute penalty well wide to deny his team victory inside 90 minutes, repeating his miss in the 2006 final which the Ivorians lost to Egypt.
The loss was another near miss for the Ivorian's golden generation, who had been expected to win African football's top prize at the last four editions but failed every time.
Two of their English Premier League players - Kolo Toure and Gervinho - missed kicks in the shootout.
"We did not play well but we also had our chances. It is a huge disappointment, we had expected a different outcome," Ivorian coach Francois Zahoui said.
Zambia, who had gone into the game as underdogs, won over the 40,000 crowd in the Friendship Stadium in the Gabon capital with their positive play against a surprisingly timid Ivorian side who failed to take the initiative in the game.
"We told ourselves we would not be scared of them. We knew we had the team to win this and we wanted to make sure we did," goalkeeper Kennedy Mweene said.
After winning, the Zambian team held up banners remembering their side that died in a air crash not far from the stadium in 1993 and whose memory they had honoured on the eve of the game.
"I can't explain why we won, it was like there was special force with us," added a teary coach Herve Renard.
At times, Zambia showed complete disdain for their star-studded opponents, with showy tricks on the ball and some clever routines although they also lived dangerously in defence.
Yaya Toure and substitute Max Gradel both went narrowly wide for the Ivorians but it was Drogba who could have been the hero after Isaac Chansa had pushed down Gervinho in the penalty area in the 70th minute and the Senegal referee Badara Diatta bravely awarded a penalty.
But Drogba hit his shot well over and then seemed to sink into a sulk for the rest of the game.
He was brave enough, however, to take the fifth penalty for the Ivorians in the shootout.
The first 14 kicks were successfully converted before a reluctant Kolo Toure had his shot saved at 7-7 but Rainford Kalaba then missed for Zambia.
Gervinho, who also did not want to take a kick, then missed before Sunzu won the cup for Zambia, who had suffered two previous defeats in the 1974 and 1994 finals.
It was the seventh Nations Cup final to be decided on penalties. The most recent was when Egypt beat the Ivorians 5-3 in the 2006 final, which also ended goalless.
