In strong 25-knot winds with waves "as big as houses" generating a tricky chop, the defending gold medallists finished fourth and first in their two "Niteroi" course races to take the overall lead.
"I think that is one of the craziest days we've been out in the 470," helmswoman Aleh said. "The waves were epic."
The New Zealanders, who are also world champions, stand in first place with six points, after benefiting from a slice of good fortune.
Britain's Hannah Mills and Saskia Clark, winners of the first test, had battled into second on the last leg of the second race before they capsized, and the New Zealand duo passed them to win.
"It was really windy with really big waves, a slight second of looking at someone else and mistiming the wave was enough to tip us in," British skipper Mills, soaked by Southern Hemisphere winter waters, said as she shivered while talking to reporters.
With four of 10 preliminary races now complete, the discard rule let New Zealanders toss aside their disqualification from the previous day, equal to a last plus one, or 21st place.
Aleh and Powrie were penalised in Wednesday's race one for failing to take a penalty turn after interfering with Austria's right-of-way.
Japan's Ai Kondo Yoshida and Miho Yoshioka are in second with eight points while Mills and Clark, who recovered for sixth after their in-sight-of-the-finish-line dunking, slipped to third overall after four races.
In other racing, the big guns used experience and brawn in tough seas to recover from mistakes in the often mystifying puffs of early races in Guanabara Bay.
Top-ranked Giles Scott of Britain, with 18 points, is first in the Finn class after finishing 11th and first on Thursday, 11 ahead of No. 2 Vasilij Zbogar of Slovenia.
In the RS:X sailboard class, 2012 Olympic champion Dorian van Rijsselberghe leads the men while No. 5 Flavia Tartaglini of Italy heads the women.
Some favourites suffered. In the Nacra mixed-sex catamaran, top-ranked French duo Billy Besson and Marie Riou stand 15th after being hampered by Besson's back problems. Australia's Jason Waterhouse and Lisa Darmanin, ranked No. 3, lead.
The men's and women's Laser classes had a day off, which could help Belgium's defending Laser Radial bronze medallist Evi van Acker recover from the effects of a gastrointestinal infection her doctors suspect was picked up on Guanabara Bay's polluted waters.
(Editing by Mark Lamport-Stokes)
