Rodallega, who joined Fulham from Wigan last month, reacted first in the box to seal victory for the Cottagers.
The visitors started well and were unlucky when Steve Sidwell's 25-yard effort was deflected over David Martin's crossbar.
The home side should have taken the lead when Luke Chadwick was fouled by keeper David Stockdale in the box and the referee awarded a penalty kick.
But Fulham were let off the hook when Shaun Williams blazed his spot-kick high over the bar.
Rodallega then punished the Dons at the other end as he reacted quickest to fire home from close range.
The home side had a golden opportunity to level it at the death but Dean Bowditch's shot whacked the top of the crossbar and Fulham held on to nick it.