Scarlets' young hooker Kirby Myhill alongside Llanelli's Liam Williams made the hard yeards before Morgan worked his magic and broke through the Argentina defence to score.
Williams' first try put Wales 17 - 0 ahead and with a dominant scrum he secured his second try in the corner.
Scarlets prop Rhodri Jones led the way with a charge in midfield from the restart which led to a try for Eli Walker.
Despite a last ditch attempt by Argentina in the final quarter, Wales brought on fresh legs to secure their fourth try.
Wales will face New Zealand on Tuesday 14 June, 17.10 at Stadio Rovigo.
Team to face New Zealand: Liam Williams (Llanelli); Iolo Evans (Scarlets /Llanelli) Owen Williams (Blues / Cardiff), Lewis Robling (Dragons /Newport), Dale Ford (Scarlets / Llanelli); Steve Shingler (London Irish), Lewis Jones (Blues / Pontypridd); Rhodri Jones (Scarlets / Llanelli), Kirby Myhill (Scarlets / Llanelli), WillGriff John (Blues/ Pontypridd), Lloyd Peers (capt, Ospreys/ Bridgend), Cory Hill (Blues / Pontypridd), Edward Siggery (Pontypridd), Thomas Young (Blues / Cardiff), Owen Sheppeard (Blues / Pontypridd).
Replacements: Jamie Sollis (Dragons / Cross Keys), WillTaylor (Ospreys / Swansea), Macauley Cook (Blues / Cardiff), Luke Hamilton (Blues / Glamorgan), Jonathan Evans (Dragons / Newport), Matthew Morgan (Ospreys / Swansea), Ross Jones (Ospreys / Bridgend)