Jason Donohue's side played some impressive stuff against a technically-gifted opponent with many players standing out in a very open game.
It was the visitors who took the lead on 10 minutes when Filip Vecheta found enough space to smash in the opener from close range.
Ireland hit back on 20 minutes through a superb solo effort from Clarke as he spun past his marker, turned inside and shifted the ball onto his left foot to slot in.
Enjoying a period of dominance, Ireland took advantage as Crowe made it 2-1 on 39 minutes after finding himself unmarked at the back post to score.
Czech Republic levelled matters on 58 minutes when Urica got his second of the game - this time ghosting in at the back post to rifle in a shot following a goalmouth scramble.
Ireland had a couple of chances to win the game and finished as the side in control, especially with the driving runs of substitute Bosun Lawal, the tireless running of Calum Kavanagh and the industry of Clarke.
The two teams will meet again on Thursday in St Kevin's Boys FC ground at 13:00.
Republic of Ireland: Patrick McGarvey; Gavin O'Brien (Fionnan Coyle 67), Oisin Hand, Anselmo Garcia MacNulty, Ronan Kilkenny; Billy Vance (Len O'Sullivan 63), Kyle Conway (Ben McCormack 62), Colin Conroy (Bosun Lawal h-t); Oran Crowe (Kailin Barlow h-t), Calum Kavanagh, Sami Clarke.
Czech Republic: David Ivanic; Filip Prebsl (Martin Vitik 50), Sebastian Novak (Roman Fukala 57), David Jambor, Lukas Endl; Krystof Danek (Tobias Cohla 63), Martin Kudela, Matej Hadas (Ondrej Sprinz 50); Adam Karabec (Daniel Langhamer 50), Filip Vecheta, Filip Urica (Jan Jelen 57).
Referee: Mark Houlihan.