The Red Devils got their tournament off to a dream start when Given Singuluma found the net inside just two minutes, picking up the ball on the edge of the box and firing home after a cross into the box was only half-cleared.
Dieumerci Mbokani wasted a fine chance to level things up shortly after as he fired his volley over the bar from all of six yards out.
Both sides had chances to add to the scoring as the first half wore on; Rainford Kalaba forcing Robert Kidiaba into stopping his well-struck free kick, before Chancel Mbemba Mangulu headed Crystal Palace winger Yannick Bolasie's cross over the bar.
Kennedy Mweene produced a fine save to keep his side's advantage intact on the half-hour mark, denying Bolasie's drilled attempt on goal with his feet.
The stopper was on hand once more shortly before the interval, this time keeping out Dieumerci Mbokani in a somewhat more straightforward manner to ensure that the Chipolopola headed into half time ahead.
A rather underwhelming second period kicked off with Mbokani missing a decent chance when he failed to get the desired contact on the ball following a cross from the right, but Congo did manage to level things up moments later through Bolasie.
The Premier League star picked out the top corner with his strike from the edge of the area on the back of some fine work by Cedrick Mabwati down the flank, cutting the ball back for the winger to smash home a deserved equaliser.
Mbokani was heavily involved again late on when he tried his luck with an ambitious overhead kick from a tight angle, which forced Mweene into making another stop.
That proved to be the last piece of action in an attacking sense, meaning that both sides had to settle for a somewhat disappointing opening-game point.