The rescue boat first lifted 90 people from the "overloaded rubber boat" and then lifted another 24 people aboard from the fishing boat.
According to volunteers, eight of those rescued were children, and eight were women, one of whom was pregnant.
"For fear of being detained by the Libyan militia, these people did not send a distress signal, putting themselves at high risk," said Sea-Eye President Gorden Isler.
Although migrants usually had to choose between Libyans and the sea, they "are now on a German ship and are finally treated like people."
This year, the number of migrant vessels increased sharply again. Many of such boats are hardly suitable for sailing at sea.