Charlton shaded possession in the early stages but it was Blackburn who had the first strike on goal when Simon Vukcevic fired wide from range.
Danny Murphy also failed to hit the target with a free kick as Charlton restricted the home side to efforts from distance.
Charlton burst forward on the counter and took the lead midway through the first half when Dale Stephens slammed into the top corner from just outside the area.
Blackburn went close soon after when Colin Kazim-Richards had a strong header well-saved before Charlton scrambled clear a dangerous corner.
The visitors held firm in the closing stages to keep alive their chances of recording a third successive league win.