England tackle Ireland, while there is a rematch between South Africa and New Zealand in Sunday's JWC semi-final lineup.
Australia 29-3 Italy
England 17-16 Argentina
With Nick Walshe changing 12 of his starting lineup, it took a last-minute Sam Olver penalty to ensure the holders an unbeaten passage to the semi-finals against a brave Argentina side at QBE Stadium, with captain and full-back Patricio Fernandez especially impressive.
George Catchpole touched down to hand England a 14-9 lead early in the second half after a suspiciously forward-looking pass from full-back Aaron Morris.
But with replacement prop Harry Rudkin in the sin-bin for collapsing a maul, the Pumas struck back, scoring a converted try through centre Emiliano Boffelli to take the lead for the first time in the game 14-16.
England pressed hard for the win in the dying minutes after Boffelli himself spilled carelessly in his own 22, and several defenders strayed offside to hand Olver the chance to win the match from straight in front of the posts.
Earlier in the day, Australia had finished their JWC campaign with a flourish as they saw off their Italian counterparts with a thumping 26-point victory in Pukekohe.
Ireland 38-0 Fiji
Wales 13-3 France
Ireland's fine form this tournament continued with an excellent victory over the young Fijians, who were notably kept scoreless, and were thrice dealt yellow cards.
Garry Ringrose has been the midfield lynchpin of the "Wolfpuppies", and he bagged 11 points from the tee as part of another impressive all-round display.
Two penalty tries, both converted by Ringrose, set Ireland on their way in the first half, with back-three flyer Ciaran Gaffney adding another after the break, before an astonishing hat-trick of penalty tries was completed with 12 minutes remaining.
Conor McKeon rounded off the scoring, converting his own try and consigning Fiji to their fate.
Wales, meanwhile, secured second spot in the Pool, but could not oust Ireland from the summit despite a hard-fought 13-3 win over the French in the Auckland downpour.
A well-taken try under the posts from Tom Williams after captain Steffan Hughes had chipped ahead proved decisive, with fly-half Angus O'Brien converting and adding a pair of penalties.
Samoa 8-21 South Afrca
Scotland 7-54 New Zealand
Having dispatched the Baby Blacks last weekend, the Baby Boks made safe their spot atop Pool C with a hard-fought 21-8 win over the plucky Samoans in Pukekohe, fly-half Handre Pollard catching the eye once more.
Aidon Davis and Nathaniel Apa scored a try apiece, with William Talataina Mu kicking a penalty for the Islanders to hand them an 8-7 half-time advantage.
But the Boks' class told after the break, centre Andre Esterhuizen and winger Sergeal Petersen going over in the final 20 minutes to confirm victory for South Africa.
Host nation New Zealand guaranteed qualification as the best runner-up from the three Pools courtesy of a thumping 7-54 victory over Scotland, extinguishing Australia's hopes of a last-four spot.
England v Ireland
South Africa v New Zealand
Both semi-finals will take place on June 15 at QBE Stadium, Auckland.