If you select one of the cells in the range to be sorted, when you click Sort, Excel will “guess” the range so I assume that this is what it is doing on your other sheet (and getting it correct by the sound of things).
There are faster ways of highlighting a range than dragging the mouse, e.g. Ctrl+Shift+arrow keys, which might make things faster.
Alternatively, if the range is always the same size, you could name the range and then type the name into the range box at the top left of your sheet.