Sergio Aguero equalized minutes later with a simple finish after Germany winger Leroy Sane capped a good team move to set the Argentine up.
The tie was a must-win for the visitors, having suffered a 2-1 shock defeat to French side, Lyon, in their group opening tie a fortnight ago.
Manchester United extend winless run in dour stalemate with Valencia
United have one more home match before the global break, with Newcastle United visiting Old Trafford in the Premier League on Sunday.
As we saw at Anfield in the Premier League last season and twice in the Champions League, this Manchester City team is not invincible and although Liverpool's front three aren't exactly on fire, nobody is expecting a goalless affair. I think the English favorited can score 3 on their own so I will play it two ways.
Hoffenheim have won just one of their previous nine matches in European competition (D3 L5), beating Istanbul Basaksehir in last season's Europa League.
Many good teams have come unstuck due to the Europa League and this is most likely what Nevin believes will be what ultimately restricts his former club. "This is one of the happiest days I have had at this club as it will help us going forward".
"I don't want to talk about the officials, I want to be on the bench, with my players in the next game", he said.
City also made an uncertain start to the second half as Florian Grillitsch's long-range effort flew just over and they survived another scare when Ederson missed a header attempting to clear a long ball from Baumann.