The match got off to a flying start as Adama Niane fired Mali in front inside the opening three minutes.
However, the lead lasted just four minutes with Jorge Rojas finding the net to bring his side level on seven.
Paraguay controlled much of the rest of the half, but they could not find a way past an inspired Germain Berthe in the Mali goal.
The second half was the opposite story as the African side took over possession, but they were kept at bay by Diego Morel.
In the end, the teams shared the spoils in a lively opening game that kept Greece top of the group.