Against the run of play, Kings Kangwa made the most of a defensive mix-up to put Zambia ahead in the 23rd minute.
Just four minutes later, the Leopards were level in the Group F match thanks to a close-range equaliser from Brentford forward Yoane Wissa.
DR Congo were awarded a second-half penalty for handball, but the decision was overturned after a video review.
Earlier in Group F, Morocco proved their credentials as pre-tournament favourites, opening with a comfortable 3-0 win over Tanzania.
DR Congo made the brighter start in an entertaining contest, dominating the early exchanges, but it was the 2012 champions who took the lead in humid conditions in San Pedro.
The opener came after DR Congo goalkeeper Lionel Mpasi veered out of his box to clear the ball into touch and collided with Leicester forward Patson Daka in the process.
The Leopards claimed he had been fouled – but Daka took a quick throw-in and Kangwa took advantage of the keeper being off his line, hitting a right-footed shot from distance which evaded two defenders and the retreating Mpasi on its way into the bottom left-hand corner.
Zambia’s celebrations had barely finished before Wissa finished off from close range after a well-timed run and pass from Cedric Bakambu – once Africa’s most expensive player.
DR Congo’s pressure continued with Zambia veteran Stoppila Sunzu – an Afcon winner in 2012 – having to clear a shot off the line from Wissa on the half-hour mark.
In the second half, Wissa broke away to send a lovely pass to Bakambu, who only had the keeper to beat but shot high over the crossbar.
DR Congo were awarded a spot-kick on the hour mark after Tandi Mwape was adjudged to have handled the ball inside the penalty area.
However, Ethiopian referee Bamlak Tessema overturned his decision after a VAR review, deciding the ball had first hit the thigh of the falling Mwape.
The Leopards, who won the Afcon title as Congo-Kinshasa in 1968 and as Zaire in 1974, pounded Zambia’s box for the rest of the match but could not find a winner.
All four Group F sides return to action on Sunday, with leaders Morocco playing DR Congo before Zambia take on Tanzania.
The second round of Afcon 2023 group games get under way on Thursday, with hosts Ivory Coast taking on Nigeria in a highly-anticipated Group A encounter after Equatorial Guinea face Guinea Bissau earlier in the day.
In Group B, Egypt and Ghana will both be looking to get their first win when they meet in Abidjan (20:00 GMT, live on BBC Three in the UK).
