The Leicester Tigers scrum-half, who ended the domestic season with a try during the Guinness Premiership Final win over Saracens, touched down in the first half in an impressive performance as England won in Australia for the first time since the historic 2003 Rugby World Cup Final.
It was a try with a Tigers flavour as Leicester colleague Tom Croft palmed down lineout ball outside the Australia 22 and Youngs burst through a gap, then round wing Drew Mitchell and dived in to the left of the posts. Toby Flood added the conversion to go with an earlier penalty as England led 10-6.
Northampton wing Chris Ashton scored the other first-half try as England led 15-15 at half-time.
Leicester fly-half Flood kicked his second penalty early in the second half, with replacement Jonny Wilkinson adding another as Lewis Moody enjoyed his first win as England captain.
Leicester tighthead Dan Cole joined Croft and Moody in the England pack, while hooker George Chuter came off the bench in the closing 10 minutes to replace Steve Thompson.
Victory tied the series 1-1 following Australia's 27-17 victory in the opening Test in Perth.
Tigers duo Marcos Ayerza and Lucas Amorosino were in an Argentina squad beaten for a second weekend by Scotland in Mar del Plata.
Former Leicester lock Jim Hamilton scored his first international try as the Scots triumphed 13-9.
Amorosino started the game on the wing to gain his fourth Test cap, while prop Ayerza made his 28th appearance for the Pumas as a front-row replacement.
Argentina are back in action next Saturday against France.
