Holders Sliema threatened first when defender Stefano Bianchardi connected with a corner but his towering header failed to hit the target.
Senglea Athletic replied with their talisman Austin Obaje-Smith who tried an attempt from just outside the box, but his curling effort could not past beyond Giuseppe Sarao.
After 29 minutes, Jonathan Pearson tried to put Sliema ahead from a set-piece, but was denied by the crossbar.
The Blues were reduced to 10-men after 37 minutes, when Jean Paul Farrugia was sent off after fouling Pablo Doffo.
The Cottonera side opened the second half on the attack, as Juninho Cabral triggered a shot from a long-range distance but Giuseppe Sarao was alert to avert the danger.
After 80 minutes, Senglea almost grabbed a late winner when defender Mark Borg connected with a corner but his goal attempt went over the crossbar, as the match headed into extra-time.
Despite the numerical disadvantage, Sliema started the extra period much stronger and Denni almost put Sliema ahead but his long-range shot was repelled by goalkeeper Jonathan Martinelli.
A few minutes later, Sliema threatened again through Ricardo Correa when he fired an angled drive, but failed to net the ball into the net.
On the brink of half-time, Senglea had two goal-scoring opportunities through Beppe Muscat and Doffo, but neither played broke the deadlock
The match headed into a penalty shoot-out and Sliema emerged winners 3-2 as Denni, Salomon Wisdom and Alex Muscat converted their penalties to put the holders into the semi-finals.