Saivet, who spent the 2018/19 campaign on loan at Turkish outfit Bursaspor, started in midfield for the last-16 clash before the 28-year-old was replaced by Krépin Diatta after 69 minutes.
Liverpool forward Sadio Mané netted the winner and also won a penalty but was denied by Uganda keeper Denis Onyango, who was already on a yellow card after bringing Mané down inside the penalty area.
Senegal, who are seeking a maiden African Cup of Nations title, will meet Benin in the quarter-finals in Cairo on Wednesday, 10th July.