Tom Mohan's side produced a disciplined and controlled performance and took the three points thanks a brilliant first half goal from Jayson Molumby.
After a solid start captain Molumby made a spectacular and decisive intervention in the 22nd minute. The Brighton midfielder curled to the roof of the Finnish net after a cross from Tyreke Wilson was only half-cleared to the edge of the box where Molumby was well-placed to collect and fire home.
Another impressive move saw Ireland progress down the left and the ball was worked back for Molumby to fire narrowly over from just outside the box in the 34th minute. Canice Carroll also fired over with a shot from distance three minutes later.
Eight minutes into the second half good Irish build up led to a chance that saw Daniel McKenna gain possession at the edge of the box and he was unlucky to send his curled effort narrowly wide across goal.
It was Molumby again threatening in the 63rd minute when he connected with a cut-back from Glen McAuley to strike at goal from 20 yards out but home keeper Johannes Luukkanen made a solid save.
Home attacker Saku Ylätupa produced a dangerous strike in the 66th minute but it whistled past Mark Travers' left upright.
Two minutes later McKenna had another long distance effort saved by the keeper then Finland went down the other end and produced a strike from Valtteri Vesiaho that skidded narrowly wide of the right post.
Stephen Mallon had a chance to extend Ireland's lead in the 73rd minute after good work by McAuley but his low strike was comfortably dealt with by the Finnish keeper.
Substitute Kian Flanagan made a brilliant burst in from the left in injury-time but was unlucky to fire into the side-netting.
With the Irish continuing to defend resolutely the final whistle blew not long afterwards and now Mohan's side can focus on their next fixture against Malta on Saturday. Malta lost 5-1 to Sweden earlier today.
REPUBLIC OF IRELAND: Travers, McKenna, Wilson, Carroll, Finnerty, Rice, Molumby, O'Connor, Mallon, Browning (Flanagan 72 ), Cregan (McAuley 51).
FINLAND: Luukkanen, Heinolainen (Mäntynen 63), Montola, Voutilainen, Vesiaho, Hyökyvirta, Eremenko (Jokelainen 71), Mohamed (Saira 63), Ylätupa, Stavitski, Kurki.
RESULTS & FIXTURES
THURSDAY, SEPTEMBER 24
UEFA U17 Championship Qualifying Group 3
Republic of Ireland 1-0 Finland, Eerikkilä-Areena, Tammela (FIN)
SATURDAY, SEPTEMBER 26
UEFA U17 Championship Qualifying Group 3
Malta v Republic of Ireland, Harju Sport Center, Lohja (FIN), 10:00 (Irish time)
TUESDAY, SEPTEMBER 29
UEFA U17 Championship Qualifying Group 3
Republic of Ireland v Sweden, Harju Sport Center, Lohja (FIN), 14:45 (Irish time)
