The Spaniard found the net for the third game in a row as Leipzig, unbeaten table toppers after four games in the Bundesliga, continued their winning ways on the European stage.
A left-back by trade, Angelino has now scored four goals in all competitions this season, helping Leipzig plug the gap left by star striker Timo Werner’s move to Chelsea.
The 23-year-old, who joined the club on loan from City last January, has flourished in a more attacking role in recent weeks, and he terrorised the Basaksehir back line during a lively first half hour on Tuesday.
"Angelino was outstanding for us in the second half of last season. He's now playing further forward and he is dangerous in front of goal," Leipzig sporting director Markus Kroesche told broadcaster DAZN.
"He feels good here and he suits the way we play football perfectly," he added.
Semi-finalists last season, Leipzig began their third Champions League campaign with a clinical performance, striking early before sitting back to defend the lead in the second half.
Both Angelino and Dayot Upamecano forced early saves from Basaksehir keeper Mert Gunok, and it was the loanee who landed the first blow on 16 minutes.
Darting into the box like a centre-forward, he picked up a chipped through ball from Emil Forsberg before turning on a sixpence around Martin Skrtel to fire a low shot past Gunok.
He doubled the lead just four minutes later, hammering in a first-time finish from just inside the box after Yussuf Poulsen launched a smash-and-grab attack from midfield.
The goalscorer dropped deeper in the second half as Leipzig soaked up pressure and Basaksehir searched in vain for a way back into the game.
The win sends Leipzig top of Group H after the first round of matches, with the Bundesliga leaders set to face Manchester United at Old Trafford in their second group game next Wednesday.