The Ulster champions trailed 1-6 to 0-6 at half-time with Robert Finnerty netting for the young Tribesmen.
Desmond Conneely added a second Galway goal to put them six points ahead while Enda McCormick's late goal was not enough for Donegal as they fell short.
Meanwhile, Mayo are through to the All-Ireland senior final thanks to a 2-13 to 0-14 win over Tipperary.
Jason Doherty and Conor O'Shea scored the decisive goals as Mayo made the final for the third time in five years.
Mayo led 1-10 to 0-7 at the break and edged clear again after Tipperary cut the gap to two points.
The Connacht men will meet the winners of next weekend's semi-final between Dublin and Kerry on 18 September.
It was a deserved win for Galway in the minor semi-final with the impressive Finnerty adding five points to his goal.
Galway go on to play holders Kerry or Kildare with the second semi-final next Sunday.
Donegal minors missed out on a place in the All-Ireland final after a 2-12 to 1-11 defeat by Galway at Croke Park.