Quelin Refalo scored the all-important goal by converting a penalty in the second half.
Dylan Falzon was sent off for Rabat late in the game.
On the other hand, Lija Athletic earned their first point as they held Dingli Swallows in a 1-1 draw.
Leontiev Konda put Dingli ahead but Erjon Beu levelled matters for Lija.