Emmanuel Mayuka put Zambia ahead with a header following a free kick in the 12th minute and Rainford Kalaba extended the lead with a clinical finish in the 20th.
Early substitute Dame N'Doye pulled a goal back with neat control setting up a near-post finish in the 74th, but Senegal ran out of time to rescue a draw.
''We knew the opportunities to score were to play behind their backs, because they have very strong players in the air,'' Zambia coach Herve Renard said. ''We did that to perfection in the first half.''
Although the lower-ranked teams claimed victories, Renard bristled when it was suggested the opening results were a surprise.
''It's not a surprise for us. It's only the result of a lot of hard work. We knew we were able to do that,'' he said. ''And we were a bit lucky in the second half because they hit the post.''
Senegal coach Amara Traore opted for a 4-3-3 formation spearheaded by Demba Ba, Mamadou Niang and Moussa Sow.
Renard was more cautious, naming just one recognized forward in his starting lineup.
That was no bar to the Zambians attacking with pace on the counterattack as Senegal's star forwards were starved of service.
The opening goal came from a set-piece. Nathan Sinkala floated a cross to the back post where the ball was returned across goal for an unmarked Mayuka to head into the net from close range.
Mayuka sprinted away to celebrate with a series of spectacular back-flips before his teammates joined him for a choreographed dance.
''It feels great (to score). We worked hard,'' Mayuka said. ''This is only the first game though and we have to keep playing well.''
Soon after, Zambia picked open the creaking Senegal defense again. Christopher Katongo strode through midfield before measuring a pass behind the defense for Rainford Kalaba to round the keeper and score.
''We had a bad start, that's why we lost and it shows you have to do more in the African Cup of Nations to go to the next level,'' Traore said.
The Senegal players looked shellshocked after the double blow which could have worsened if goalkeeper Bouna Koundoul hadn't raced out of his box to deny Mayuka with a sliding challenge.
Mayuka, proving a constant threat to the Senegal backline despite playing on his own up front, cut in from the right and fired a fierce left-footed drive that brought a full-length save out of Koundoul in the 40th.
Sow wasted two early chances to cut the deficit for Senegal but shot wide both times in the opening 10 minutes of the second half.
Zambia's tempo dropped as the second half wore on and Ba fired wide as the ball bounced to him following Kader Mangane's header across goal from a free kick in the 65th.
Senegal finally found a reward for its increasing dominance when Dame N'Doye controlled Guirane N'Dawe's floated pass in the box and shot inside the near post.
Group A continues with Libya vs. Zambia and Equatorial Guinea vs. Senegal on Wednesday. Group B matches start on Sunday.