Stephen O'Donnell fired over the bar in the first minute, while Jonathan Minnock was also off target with a free kick and Barry Curran had a left-footed cross held by Rovers 'keeper Barry Murphy.
For the visitors, David Cassidy succeeded only in directing his shot from the edge of the area into James Gallagher's arms after Eloka Asokhu's attempted clearance fell into his path.
The home side can count themselves somewhat unfortunate not to have made the telling breakthrough in the early exchanges of part two as Gorman's side were out of the blocks quickest after the break.
Matthew Crossan had a shot held by Murphy while Eloka Asokhu headed Michael Funston's cross wide of the post, before Harps came within a lick of paint of edging in front.
The hosts were awarded a free kick on the right side of the penalty area in the 52 nd minute and David Bell stepped up, but his effort struck the butt of Murphy's right hand post.
Andy Myler missed a good chance for Rovers when he shot wide from a good position, but on 58 minutes the Hoops did grab the all-important opening goal of the game.
A slip by Jonathan Minnock allowed Jamie Duffy time on the right and his perfect cross was met by the in-rushing Padraig Amond who headed into the far corner past James Gallagher.
Harps were dealt a further blow on 75 minutes when they were reduced to ten men when Barry Curran was dismissed for a foul on David McGill meaning he will be suspended for Harps' next game which is away to Dundalk on Friday night next.
After this, there was only going to be one winner as Harps failed to trouble Barry Murphy, apart from a late effort from Michael Funston which the Rovers net minder gathered with ease.
So, defeat again for Harps, whose challenge for promotion is now all but over and it now remains a case of just playing out the season for the boys in blue who, at the turn of the year, had high aspirations of making a push to go up.
Finn Harps: James Gallagher; Shaun McGowan, David Bell, Eloka Asokhu, Shane Bradley; Barry Curran, Michael Funston, Matthew Crossan, Jonathan Minnock; Davitt Walsh, Stephen O'Donnell. Subs: Darren Meenan (for Walsh, 64mins); Shane O'Connor (for Asokhu, 68mins); Ryan McGavigan (for Crossan).
Shamrock Rovers: Barry Murphy; Ger O'Brien, Robbie Clarke, Aidan Price, Ray Kenny; Paul Shields, Jamie Duffy, David Cassidy, Davy O'Connor; Tadgh Purcell, Andy Myler. Subs: Padraig Amond (for Purcell, 30mins); David McGill (for O'Connor, 64mins).
Referee: Richie Winter