The French midfielder came off the bench for Ryan Christie at the Stadio Olimpico in the second-half with the game at 1-1, after James Forrest's strike had cancelled out Ciro Immobile's early opener for the home side.
As both sides went for the winner Ntcham latched on to an Odsonne Edouard pass in the fifth of five added minutes and dinked the ball over goalkeeper Thomas Strakosha to guarantee Celtic a place in the last-32 of the Europa League with two Group E fixtures remaining.
It was also Celtic's first win on Italian soil in 13 attempts and Ntcham told the club's Youtube channel. "I didn't know that but it is good news for everybody.
"It is a great feeling and I am really happy for my team and for myself too. It was a difficult angle but I was really proud of my finish.
"It was a brilliant atmosphere and I think everybody is happy now. We managed the game better in the second-half.
"We started the game a bit slow but after the first goal we scored, we got into the game.
"It was a good game to play in and the supporters can be really proud of the team."
Celtic skipper Scott Brown described the victory as "exceptional".
The midfielder said: "We have managed to qualify after four games, it shows you how hard we have worked.
"It is the first time any Celtic side have won on Italian soil and it means a lot to us.
"They have a great team, they have great players and players who are worth a lot of money.
"It shows what a good quality team we are as well."