The Congo DR outfit appeared to be set for defeat after Brazilian attacker Sergio Junior found the net for the hosts in the 19th minute.
Proceedings were briefly brought to a halt midway through the second half as a sandstorm hit the stadium in Khartoum, reportedly leaving a number of fans injured.
There was to be a twist in the tale after the game resumed, as midfielder Mabidi converted from the spot in the 88th minute to earn his side a share of the spoils.
The result sees both Al Hilal and Vita Club move to four points in Group A, although they can be overtaken if there is a winner in Sunday's meeting between Zamalek and TP Mazembe, who currently boast three points apiece.
The two clubs will play the reverse fixture in Kinshasa on July 25.