Morgan slotted home the first of six kicks after three minutes before adding a superb solo score.
Liam and Owen Williams as well as hooker Kirby Myhill made the hard yards before Morgan worked his magic and ghosted through the Argentina defence to score.
Williams then crossed for a second try to put Wales 17 v 0 ahead. Richard Webster's side dominated in the scrum, and when the ball was sent wide in the 25thminute, Williams crossed in the corner for a converted try.
Argentina clawed back a score before half time, scrum half Marcos Bollini going over in the corner.
From the restart, Wales showed more urgency and intent. Scarlets prop Rhodri Jones led the way with a charge in midfield. From the ensuing ruck, Morgan kicked ahead for Eli Walker to chase and touch down.
Argentina got a penalty and slowed down the game for the third quarter, but Wales brought on some fresh legs and got their fourth try through Williams after 68 minutes.
Good line-out ball went through the phases quickly, creating an overlap on the left for Williams to glide over. Morgan converted and slotted a second penalty to take the score to 34-8 with ten minutes to go.
Wales head coach Richard Webster said, "We are pleased with how the game went, our game-plan worked well.
"We still have areas in which we can improve, and we will have to up our game for New Zealand on Tuesday."
Matthew Morgan, Liam Williams (2), Eli Walker
Cons: Matthew Morgan (4)
Pens: Matthew Morgan (2)
Pens : Ormson
Steve Shingler (London Irish); Liam Williams (Llanelli), Owen Williams (Blues /
Cardiff) (Iolo Evans Scarlets / Llanelli), Lewis Robling (Dragons / Newport), Eli Walker (Ospreys / Swansea); Matthew Morgan (Ospreys / Swansea (Rheon James Scarlets/ Carmarthen Quins), Jonathan Evans (Dragons / Newport) (Lewis Jones Blues / Pontypridd); Rhodri Jones (Scarlets / Llanelli), (Lewis Smout Blues / Pontypridd), Kirby Myhill (Scarlets / Llanelli) (WillGriff John (Blues/ Pontypridd), Will Taylor (Ospreys / Swansea), Macauley Cook (capt, Blues / Cardiff) (Lloyd Peers Ospreys / Bridgend), Cory Hill (Blues / Pontypridd), Edward Siggery (Pontypridd), Luke Hamilton (Blues / Glamorgan), Ben Thomas (Ospreys / Bridgend) (Owen Sheppeard Blues / Pontypridd)