Despite entering their maiden continental adventure, Oliver Glasner's side are adapting at a rapid pace. Without star players like forward Jean-Philippe Mateta and wing-back Daniel Muñoz, the Eagles left Dublin with a comfortable win that all but guarantees them a spot in the Europa Conference League playoffs.
Another victory in their upcoming fixture against Finland's KuPS should be enough to seal straight passage to the last 16, particularly after a previous setback against Strasbourg.
This occasion offered a platform for several Palace's lesser-used players to impress. Christantus Uche, in only his second start since arriving on loan from Getafe, opened the scoring with a well-taken finish. Striker Eddie Nketiah contributed a another, finding the net for the second game in match.
The Shelbourne team that had concluded their league season were no match even for a largely rotated Palace outfit. The Londoners were further depleted by the reports that Mateta and Muñoz are sidelined with knee injuries.
In spite of torrential rain in Dublin, Palace quickly established dominance. A flowing passing sequence in the 11th minute, sparked by Daichi Kamada's incisive pass, allowed Nketiah to set up Uche for a simple tap-in.
Youngster Adam Wharton went close soon after, driving a long-range shot over the bar. Nketiah subsequently appealed for a penalty after racing into the area, but the referee waved away the appeals.
Ex-Arsenal man did not have wait long to get his goal, tapping home from a yard out after Uche's effort had hit the post.
The home side were hanging on desperately. Full-back Kameron Ledwidge was fortunate to avoid a booking for two agricultural challenges on Yeremy Pino, before Chris Richards rattled the woodwork with a powerful header from a corner.
The match was as good as over eight minutes from half-time. Yeremy Pino meandered past a series of comically weak challenges before calmly dispatching a shot past keeper Wessel Speel to extend the lead to 3-0.
After the break, manager Oliver Glasner took the chance to rest key individuals like Kamada and Wharton. Replacement Romain Esse came close to scoring his very first touch, but saw his effort blocked.
The youngster was desperately unlucky later on, seeing one shot crash off both posts before being clasped on the line. Uche also blazed a sitter of a chance, indicating there is still scope for improvement in his game.
The only worry for Palace was a second-half injury to Justin Devenny, who limped off. This allowed 17-year-old striker Benji Casey to make his senior debut, capping an otherwise perfect evening for the traveling side.
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