Friday's game saw Rovers start nervously in front of what was a typically partisan Hoops support, but they found themselves a goal up on the quarter-hour mark and Pat Scully must have been thinking that Christmas had come early for his side after being gifted the opener.
Shane Bradley's attempted back-pass to James Gallagher, bypassed the Harps net-minder and Andy Myler won the race to the loose ball to prod home from an acute angle.
The Hoops had an opportunity to double the advantage on 28minutes when Tadhg Purcell caught Shaun McGowan napping, but the striker's powerful effort was well beaten out by Gallagher.
In between times, Harps had a couple of half chances to get back on a level footing, but Eloka Asokhu flicked a Minnock cross wide of the target and Matthew Crossan was also wide with a left-footed shot from just inside the box.
This was, unfortunately, as good as it would get for Harps, although that 15 th minute strike from Myler was all that separated the sides at the interval. Rovers may feel that they should have been two up on 28minutes when Tadhg Purcell was denied by a fine stop from Gallagher after he capitalised on hesitant defending.
After the break, it was the home side who settled quickest and they eventually added to their tally, but were made wait until just after the hour mark before the elusive second was netted.
A deep cross from the left found its way to the back post and the in-rushing Derek Pender nipped in to powerfully head past James Gallagher to send the home crowd into raptures.
With the Hoops fans in full voice, their side added two more in the closing stages to put a gloss on what was a famous night for them, while at the same time compounding on the misery of Harps.
Tadhg Purcell added number three in the 85 th minute when he rose highest in a crowded goalmouth to head home and substitute David Cassidy found the far corner with a neat right-footed effort two minutes into added time.
Shamrock Rovers: Barry Murphy; Ger O'Brien, Robbie Clarke, Aidan Price, Ian Ryan; Ray Kenny, Derek Pender, Paul Shiels, David McGill; Tadhg Purcell, Andy Myler. Subs: Paul Gannon (for Clarke, 56mins); Gerard Rowe (for Myler, 76mins); David Cassidy (for McGill, 81mins)
Finn Harps: James Gallagher; Shaun McGowan, David Bell, Eloka Asokhu, Shane Bradley; Michael Funston, Jonathan Minnock, Matthew Crossan; Gary Crossan Stephen O'Donnell, Davitt Walsh. Subs: Darren Meenan (for Bell, 68mins); Johnny Gallagher (for O'Donnell, 81mins).
Referee: Tom Connolly (Dublin).