Donegal began well with an early goal from Patrick McBrearty.
But Galway came back into the game and at the break it was Donegal 1-4, Galway 0-7.
Ryan McHugh put Donegal into a 2-9 to 0-9 lead midway through the second half with Colm McFadden and Michael Murphy impressing.
Substitute Christy Toye got the third goal late on to delight the big Donegal support.
Donegal now face Mayo in the quarter-finals.