"That was totally great, I am totally proud of the team," said German trainer Silvia Neid.
Simone Laudehr, who was carrying a knee injury, shot the winning goal in the 26th minute.
The team seemed significantly more engaged with the match and concentrated than they had in the previous match which they lost 0-1 against Norway. That was the first defeat for the German women in a European championship match for at least 20 years.
"We held out well against the aggressive, well-trained Italians, and we fought with everything we had," said Neid.
The team will play against Sweden in the semi-final - but without top forward Celia Okoyino da Mbabi, who strained a muscle in her right thigh.
The Swedish match on Wednesday should be a humdinger, said Neid, as the Swedes will have the advantage of a home crowd.
"The Swedes have a very strong team and are favourites. But why should our young team be scared of them?" asked Neid.
Sweden got through to the semi-final with an effortless 4-0 victory against Iceland.