Blues striker Morrison was involved in the only goal of the game scored five minutes from full-time at Landsdowne Road by Charlton midfielder Matt Holland.
The impressive Liam Miller played a superb ball out to Morrison on the right flank and his cross was met sweetly on the volley by Holland to fire past Romanian substitute keeper Stelea from just inside the box.
The Ireland squad now travel to London for a triangular tournament at Charlton Athletic's Valley ground where they play against Nigeria and Jamaica on May 29th and June 2nd respectively.
Republic of Ireland: Given (Newcastle); Finnan (Liverpool), O’Brien (Newcastle), Cunningham (Birmingham City), Maybury (Hearts); Miller (Celtic), Roy Keane (Manchester United), Holland (Charlton), Reid (Notts Forest); Morrison (Birmingham City), Robbie Keane (Tottenham). Sub: Rowlands (QPR) for Reid (78 mins).