Christantus Uche, Eddie Nketiah and Yeremy Pino scored in Dublin to send Palace to within a point of eighth-placed Mainz.
Palace end their league phase campaign by welcoming Finnish side KuPS next Thursday.
Irish outfit Shelbourne are third from bottom in the table after securing just one point from five matches.
Palace, who have lost just twice since November 1, named a strong side despite Sunday’s Premier League game with second-placed Manchester City, but coach Oliver Glasner left attacker Jean-Philippe Mateta out of the matchday squad.
Nigeria’s Uche opened the scoring after 11 minutes before Nketiah doubled the advantage 14 minutes later.
The three points were secured eight minutes before the break as Spain international Pino scored his third goal of the campaign.
Elsewhere, a much-changed Strasbourg claimed their last-16 berth with a 1-0 win at Aberdeen. (AFP)