Quicksort: Sort two Columns

I would like to sort a table using Quicksort. However, when doing so, I do not want to consider only one column, but two columns at the same time. In other words, I would like to order by the first column first and in case that the first column has the same value, I would like to sort within this value the second column.

For example, like that:

Column 1  Columns 2
A         A
A         B
A         C
B         A
B         B
B         C
C         A
C         B

My first attempt was to apply the Quicksort algorithm two of the first column first and after that to the second column. Unfortunately, this leads to the problem that after the second column has been sorted, the values from the first column are messed up again.

How can I achieve that the values of both columns are ordered correctly and that the order of the first sorted column remains even after sorting the next column?