The club from the Democratic Republic of Congo went into the encounter on the back of a tragic domestic encounter with rivals TP Mazembe last weekend, which saw 15 fans killed when crowd trouble was followed by a stampede.
In Vita's win on Sunday, Ndombe Mubele opened the scoring in the 19th minute, putting five-time African champions Zamalek on the back foot.
The away side managed to draw level with 14 minutes remaining when Momen Zakaria found the net, but Emmanuel Ngudikama swiftly restored his side's lead to give Vita a winning start.
Sunday's other match saw Tunisia's CS Sfaxien beat Al Ahli Benghazi 3-1 at Stade Taieb Mhiri in Group B.
Fakhreddine Ben Youssef and Ferjani Sassi both went close early on for the hosts, but they did not have to wait too long for a breakthrough as Ali Maaloul set up Taha Khenissi to score in the 15th minute.
A Bassem Boulaabi own goal pulled Al Ahli level 12 minutes later, only for Mahmoud Ben Salah to fire Sfaxien back in front soon after, with Maaloul grabbing another assist.
Substitute Ghazi Chellouf got on the scoresheet four minutes from time to secure victory for the Tunisians.
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