Ryan himself went close to doubling the advantage, but his effort from long range was just over Gavin Cullen's crossbar.
Harps, to be fair, had their moments, but they couldn't find a breakthrough in the opening period. When they did get a sniff of the target, they couldn't capitalise with Davitt Walsh seeing an effort from close range saved by the 'keeper and Matthew Crossan sending the follow up well wide.
On the hour mark, Shels doubled the lead and it was again Byrne who was the scorer. The big front man headed Dave Rogers' deep cross beyond the reach of Cullen for his second of the evening.
Glen Crowe, who was brought on from the bench, then got in on the act with 66 minutes on the clock. The ex-Bohemians front man appeared to be in an offside position when he got possession, but the flag stayed down and he rounded Cullen to tap home.
Cullen was forced out of the action after colliding with Crowe as he attempted to stop him from going through and his place was taken by James Gallagher.
The Gorthahork man wasn't long on until he was picking the ball out of the net after being beaten by a superb strike from Greg O Halloran.
O' Halloran picked up possession and took a superb touch to get him round Sean Cooney before unleashing a cracking effort from over 20 yards past the despairing reach of the Harps netminder.
Harps got a late consolation when Chris Malseed finished off a nice attacking move from his side. It was too little, too late for them however and they now prepare for League action again and the long trip to Cobh on Saturday next.!
Shelbourne: Dean Delaney, Owen Heary, Dave Rogers, Jamie Harris, Sean Dillon, Alan Reynolds, Ollie Cahill, Alan Moore, Stuart Byrne, Jason Byrne, Bobby Ryan.
Finn Harps: Gavin Cullen, Shaun Mc Gowan, David Bell, Sean Cooney, Eloka Asokhu, Chris Malseed, Matthew Crossan, Anthony Gorman, Jonathan Minnock, Conor Gethins, Davitt Walsh.
Referee: Richard Winter
Harps MOTM: Chris Malseed.