Bohemians advance to face either FK Riga of Latvia or Israel's Fylkir in the second round (5/6 July and 12/13 July).
Scotland's Hibernian are potential third-round opponents, those games to be played on 19/20 July and 26/27 July.
The eleven successful teams from Intertoto Cup qualifying will go on to enter the second qualifying round of the Uefa Cup.
Rhyl: John Gann, Paul O'Neill, James Brewerton, Carl Ruffer, George Horan, Craig Jones, Gareth Wilson, Mark Connolly (Craig Garside 80), Chris Roberts (Jimmy Kelly 63), Marc Lloyd Williams, Gary Powell. Subs not used: Greg Stones, Tom Roberts, Matthew Holt.
Goals: Connolly 37, 41.
Bohemians: Brian Murphy, Owen Heary (Thomas Heary 63), Kevin Hunt, Ken Oman, Mark Rossiter, Harpal Singh, Jason McGuinness, Stephen O'Donnell, Glen Crowe (Darren Mansaram 76), John Paul Kelly (Michael McGinlay 42), Jason Byrne. Subs not used: Chris Konopka, Neale Fenn, Chris Turner.
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