The visitors knew they had to take the game to Larne and start fast, which is exactly what they did as they hit the front after 11 minutes.
Mengucci's strike from an acute angle went through the legs of Rohan Ferguson and into the bottom corner, stunning the Inver Park crowd early on.
The Irish Premiership champions responded midway through the first half as Ridley met Ronan Doherty's deep in-swinging free-kick with the easiest of headers from close range to level for the hosts.
From then Larne began to flex their muscles, but couldn't quite find a way past Michele Nardi for a second time before the break.
The visitors finished the first half the stronger of the two sides and had the ball in the net through Romeo Bertani before it was ruled out for offside.
Tre Fiori then came close once more on the stroke of half-time, this time through Nico Manara, whose header whistled past the far post.
The visitors' task got even more difficult when they were reduced to 10-men as Rea was shown two yellow cards in quick succession midway through the second half.
Larne then went ahead for the first time on the night from the penalty spot, as Bent found the top right-hand corner after Matty Lusty was brought down just inside the area.
Substitute Mohamed Ben Kacem missed a glorious chance to make it a nervy finish for Larne, but fired over the crossbar from inside the six-yard box.
The visitors were then reduced to nine men late on as substitute Bernardi picked up two yellow cards in a matter of seconds.
Substitute Paul O'Neill then thought he had put the icing on the cake with a third goal right at the death, but the linesman flagged for a foul in the build-up.
Larne will now look forward to their tie against Serbian giants Red Star, with the first leg to take place at Inver on Tuesday, 21 July and the second leg away on Tuesday, 28 July.