Boateng, who joined Bayern from City in 2011, broke the deadlock in Munich with a powerful shot after the Germans controlled the game, but could not find a way past visiting keeper Joe Hart, who made several superb saves, until the 90th minute.
“I think we had a lot of chances, we wasted many, but we believed until the end,” Germany international Boateng told reporters. “The ball came perfectly and I just drilled it in…
“We deserved to win, although City made a good game but it was us who had the chances and it is extremely important to start off with a win.”
City, who had come back from two goals down to beat Bayern 3-2 in Munich in the group stage last year, were mostly on the back foot but successfully kept the Germans at bay, with Hart doing his best to keep the scores level until the last minute.
Roma are top of the group on goal difference after crushing CSKA Moscow 5-1.
“It was important for the team to win,” said Bayern coach Pep Guardiola. “We played well and it was deserved and I am happy to have got the three points. Don’t forget we were playing against Manchester City.
“We played better. We had problems initially to control the game but then we improved. I am satisfied with our performance.”
Bayern, with winger Franck Ribery out injured and Arjen Robben on the bench, were slow out of the blocks as both teams cautiously tried to get a foothold in the game.
There were four changes for City from the team which drew 2-2 with Arsenal on Saturday with suspended Pablo Zabaleta replaced by Bacary Sagna and Yaya Toure, Samir Nasri and Edin Dzeko earning starting spots.
The hosts gradually got on top and almost took the lead when Thomas Mueller sneaked into the box, but Hart parried his powerful header over the bar in the 20th minute.
Seconds later the England keeper pulled off another sensational save to palm Mario Goetze’s deflected effort past the post before City responded with a curling Edin Dzeko shot that sailed narrowly wide.
The English champions, with suspended coach Manuel Pellegrini in the stands and his assistant Ruben Cousillas alone on the bench, successfully closed down space to keep Bayern at bay outside the penalty area.
David Alaba tried his luck twice from long range but again Hart was on hand to rescue his team.
The Bavarians increased the pressure in the second half but had problems cracking open a tight City defence.
The introduction of Robben and forward Claudio Pizarro late in the game helped provide an added impetus and Bayern’s pressure finally told when Boateng fired home.
“We fought hard all night against a good team and we had chances all night,” keeper Hart said.
“We knew we going to be in for a tough game. The goal has come from a deflection in the end, and Jerome has come back to haunt us. I think a draw would have been good.”