In Sunday's other game, multiple former champions Al Ahly of Egypt beat Wydad Casablanca 2-0.
A goal from Ethiopia international Saladin Said was enough to give the home side a victory in front of their home fans in Addis Ababa on Sunday.
Said's 60th minute strike helped the Ethiopian side boost their hopes of reaching the knock-out phase of the competition, moving them into second place in Group C.
Saint George are two points adrift of leaders Esperance of Tunisia who beat defending champions Mamelodi Sundowns 2-1 in South Africa on Saturday.
AS Vita Club - who were crowned African champions in 1973 - are bottom of the Group C standings, yet to register a single point.
In Group D, Al Ahly - the eight-times champions - secured a 2-0 win over Morocco's Wydad Casablanca at the Borg Al-Arab stadium near Alexandria.
Moemen Zakareya put them in front after 24 minutes and Junior Ajayi secured the victory with just over 10 minutes to go.
Ahly go top of the pool on goal difference over Zambia's Zanaco - with both tied on seven points from three games so far.
Ethiopia's Saint George defeated AS Vita Club of the DR Congo 1-0 in the latest round of group games in this year's African Champions League.