The Cape Winelands side came into the clash on the back of a dramatic late win over AS Otoho last weekend, while Singida were aiming to bounce back from their 2-0 defeat to CR Belouizdad in Algeria.
Steve Barker made a few tweaks to his line-up, including recalling Oscarine Masuluke, who was called into action midway through the first half to keep out a threatening effort as the hosts began to dictate the tempo.
Stellenbosch, however, struggled to impose themselves in possession and created little in the way of clear opportunities in the opening 45 minutes.
After a goalless first half, Stellies struck first seven minutes into the second stanza. Phili, making a milestone appearance, continued his impressive form by netting his sixth goal of the campaign to hand the visitors the lead.
Barker introduced fresh legs after the hour mark, bringing on Andre de Jong and Chumani Butsaka for Cupido and Thato Khiba as Stellenbosch looked to maintain their advantage.
But the Tanzanian outfit mounted a late surge and their pressure paid off in the 90th minute when Marouf Tchakei calmly slotted home a penalty to level matters and secure a point for Singida.
Stellenbosch now shift their attention to Wednesday's Betway Premiership fixture â their final outing of the year.