The French side had lost 2-0 in Cyprus last week, and despite a spirited effort tonight, it is Limassol who progress.
They almost found a second after a similarly quick start to the second half, but Valentin Eysseric's curling effort was tipped wide.
The hosts were denied a big penalty claim midway through the half when Eric Bautheac went down, but the referee waved play on.
Limassol did an excellent job of thwarting Nice's attacks after that and almost equalised late on through Gaston Sangoy, but Nice were able to clear.
It did not matter though, as the Cypriots had done enough in the first leg, and held out for a 2-1 aggregate win.