The Irish scored six tries in total to finish runners-up behind the South Africa President’s XV.
Morris, who played his third full 80 minutes of the tournament, swooped on a loose pass on halfway before galloping away for Emerging Ireland’s bonus-point try four minutes into the second half.
And he grabbed his second four minutes later, scooting away from four defenders on a jinking run to the line.
Fly-half Ian Keatley converted all six tries, including two of his own, and there was also a try each for Tiernan O'Halloran and Niall Annett, as the Irish led 42-14 by the hour mark.
However, a strong final quarter for Uruguay saw them claim three tries to end the tournament on a high.
Logovi’i Mulipola came on as a second-half replacement for Samoa in their 39-10 victory over Martin Castrogiovanni’s Italy on Saturday.
Samoa, who included former Tigers winger Alesana Tuilagi in their ranks, outscored their opponents five tries to one.
It was third successive Test win for Samoa against Six Nations opposition after victories against Wales in November and Scotland last week, and secured their place in the final of the South African Incoming Series.
Samoa captain Paul Williams scored all their points in the first-half with a converted try and a penalty as they led 10-3 at the break.
Samoa scored two more tries early in the second half through wing Alapati Leiua and centre Johnny Leota.
Former Tigers prop Castrogiovanni was withdrawn by the Azzurri after 59 minutes, shortly before Mulipola came on and No8 Taiasina Tuifua grabbed a fourth try for Samoa.
Italy were awarded a penalty try nine minutes from time as they attempted to drive a scrum over from close-range before Samoa fullback James So'oialo completed the scoring with a try in the 74th minute.