Having lost the first leg 1-0 at the Stade Regional de Nyamirambo, Shendi secured a 1-1 aggregate score when Ahmed Adel bagged in the 90th minute at the Khartoum Stadium.
But their hopes of progression were curtailed by a devastating loss in the shootout, as Kigali moved on to the next round.
Kigali will be joined by Tunisian outfit Etoile Sahel, who overcame a 1-0 deficit from the first leg to come through 3-1 on aggregate against Cara Brazzaville.
It took 25 minutes for the hosts to break the deadlock, as Saif Ghezal opened the scoring the level the tie.
Mohamed Slama doubled the advantage on the night 12 minutes later, and handed Sahel the lead for the first time over the two legs.
The comeback was complete just three minutes after the break as Hamza Lahmar bagged from the penalty spot, ensuring there would be no way back for Brazzaville.
