Two days after losing the league to San Giljan, Neptunes were able to beat Sliema in the KO quarter-final.
The regular time finished in a draw, and a penalty shoot-out was required to establish the winner.
In the other quarter-final match, Sirens beat Birzebbuga.
The semi-finals - Neptunes vs Exiles and San Giljan vs Sirens will be played on Thursday.
The final will be played on Sunday.