At the other end, Barry Murphy was out well to deny Chris Breen after a good through ball from Malseed.
Rovers edged in front after 37 minutes when Jamie Duffy smashed home past Boyle from an unmarked position at the back post.
Moments later, David O Connor came close to doubling the advantage, but his left-footed drive flashed across goal before being eventually cleared to safety.
Just two minutes had elapsed in the second half when Rovers did get that all-important second goal. Philip Sheppard's cross from the right found debutant Anto Flood at the back post and his header downward gave Boyle little chance.
Davitt Walsh should have done better when afforded a good chance of pulling a goal back soon after. Eloka Asokhu's free kick was flicked into his path by Shane Bradley, but he failed to connect properly and the save was easy for Murphy.
In the final minute, Jonathan Minnock – who is homing in on Jim Sheridan's record haul of appearances for Harps –had a free kick well tipped over by Murphy.
This was about as close as Harps came and certainly they will have been disappointed not to be heading back to the Northwest with at least a point.
Rovers, however, were full value for their win and they could have added a third in the closing stages, but Jamie Duffy fired wide from a good position at the back post.
The defeat will be frustrating for Harps supporters, but a return of six points in three games against the Division's top three is not a bad return and the hope remains that the corner can be turned in the coming weeks.
Harps now have two home games on the trot to look forward to. Dundalk visit Ballybofey this coming Saturday, before Athlone come to the banks of the Finn next weekend.
Shamrock Rovers: Barry Murphy, Ray Kenny, Robbie Clarke, Aidan Price, Ian Ryan, Vinny Perth, Jamie Duffy, Mark O Brien, Tadhg Purcell (Anto Flood, 34), Philip Sheppard (Willie Doyle, 86), David O Connor (David Cassidy, 79).
Finn Harps: Michael Boyle, Shaun Mc Gowan, David Bell (Ryan Mc Gavigan, 84), Eloka Asokhu, Shane Bradley, Chris Malseed, Chris Breen, Jonathan Minnock, Conor Gethins, Davitt Walsh (Stephen O'Donnell, 62), Sean Cooney (Shane O'Connor, 68).
Referee: Mr. D. Tomney
Finn Harps Dot Com Man Of The Match: Harps had few performers last night who would have been in contention for this award. Up front, there was a distinct lack of bite, while the backline was shaky, to say the least, at times. Jonathan Minnock battled hard in the middle of the park, while Sean Mc Gowan gave his typically tigerish performance at right-back. The award goes to David Bell, though. The Inishowen man was full of effort and more often than not, his forays forward were in vain as his team mates failed to pick out several of his good runs from full-back.