In the first of two games in Waterford, James Scott's team were led out by Peamount United's Della Doherty and made a bright opening with their intention to play quick, attacking football.
However, it was the visitors who opened the scoring through No 20 Amanda Jacobsen Andradottir and they held onto that lead going in at half-time.
Molloy hit back though on 57 minutes to draw the scores level after the Thomastown United youngster wasted little time in finishing when in front of goal with a left-foot finish.
Iceland got their second goal seven minutes later through substitute Anita Yr Porvaldsdottir, but Molloy broke Icelandic hearts on Valentine's night by finding the back of the net again in the 75th minute.
These two games are being used as preparation for next month's UEFA European Championship Elite Round qualifiers, which will also be held in Waterford.
Ireland had scored 21 goals in the Qualifying Round but now they must take on Denmark, Serbia, and Austria if they are to reach the finals tournament in Sweden.
Next up is a Sunday afternoon showdown in Tramore AFC with kick-off set for 14:00. Scott will be eager to use the game to test more players in his squad and continue to work on their positive play.
Republic of Ireland: Hayes Coen (Askalnyte 57); Slevin (Slattery 57), Doherty, Brennan, Kinneavey (Stapleton 72); Clancy, Devanney (O'Dowd 57), Molloy; Horgan (Fitzpatrick 51), McLaughlin (Corbet 51), Brown (Watkins 72).
Iceland: Olafsdottir; Hjorvarsdottir, Sigurbjornsdottir, Petursdottir, Agustsdottir, Asmundsdottir, Kristinsdottir, Olafsd.Gros, Siguroardottir, Nielsdottir, Andradottir.
Referee: Clare Purcell.