Ireland reached the quarter-finals in 2000 and 2008 but did not win a match at the previous World Cup in 2013.
Former Wakefield player Kay, who scored 27 tries in 21 appearances for Toronto this year, opened Ireland’s account after only two minutes on Sunday following a good pass from full-back Scott Grix.
Seven minutes later loose forward George King timed his run to perfection to touch down Michael McIlorum’s grubber kick, and Finn kicked his second conversion before adding an 18th-minute penalty to open up a 14-0 lead.
Kay grabbed his second try in almost identical fashion to his first and Finn maintained his accuracy to land his fourth goal.
Ireland coped admirably with the conditions, aided by drinks breaks after 20 and 60 minutes, but suffered a setback three minutes before half-time when Grix’s pass in a promising attacking position was intercepted by centre Justin Castellaro, who raced 70 metres to score.
Former Hull KR winger Josh Mantellato added the conversion to make it 20-6 at half-time, although Italy lost half-back Jack Johns – son of former Wigan player Matthew – with an arm injury.
The deficit was cut to eight points six minutes into the second half when Mantellato outjumped Shannon McDonnell to put centre Nathan Milone over for Italy’s second try, which Mantellato converted.
However, Ireland quickly regrouped to make the game safe with two tries in a 13-minute spell.
Prop Kyle Amor charged onto McIlorum’s short pass to score their fourth try and centre Michael Morgan touched down a kick from Grix after Italy full-back James Tedesco was deceived by a wicked bounce.
Finn kicked his sixth goal but failed to convert a last-minute try from McCarthy-Scarsbrook, who powered over from 10 metres to cap an outstanding individual performance in which he carried the ball 195 metres, the second most of any forward in the past three World Cups.
Ireland: Grix; McDonnell, Chamberlain, Morgan, Kay; Pewhairangi, Finn (capt); Singleton, McIlorum, Amor, McCarthy-Scarsbrook, Roberts, King
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