The increase was led by an 18.9% surge in whole milk powder prices, while prices for other products also rose, albeit more modestly.
The result followed another strong outturn two weeks ago and meant WMP prices had now risen almost 30% in the last month and were back to levels last seen in October last year, Westpac senior economist Anne Boniface said.
While the recent strength in prices would ''certainly bring a smile to the face of farmers'' in the beleaguered dairy sector, the bank continued to sound a note of caution.
''We have seen periods of strong gains in dairy prices followed by partial retracement in the past. A year ago we saw solid price gains through August-September which partially reversed later in the season,'' she said.
However, the fundamentals did appear to finally be shifting in favour of dairy producers. Globally, growth in milk supply continued to moderate, most notably out of Europe but also elsewhere.
But, perhaps more promisingly for farmers, there were signs the most recent price rise coincided with a lift in Chinese demand.
BNZ economist Doug Steel, who described the latest auction result as ''extremely strong'', said there was now clear and present upside to Fonterra's 2016-17 forecast of $4.25.
''If dairy product prices maintain these levels, and the NZD doesn't push materially higher, then the milk price would likely be over $5,'' he said.
On the back of the strengthening international prices, BNZ had lifted its milk price forecast from $4.60 to $5.30.
The bank sensed the latest auction result had ''a bit of panic buying in it''. Unsatisfied bidders had been a bit elevated of late and the 6.6% price rise at the previous auction probably generated some fear of missing out at this week's event, he said.
Mr Steel suspected the market was now factoring in a sizeable decline in New Zealand milk production.
ASB rural economist Nathan Penny said the bank was sticking with its $6 milk price forecast for 2016-17.
The lift over the two August auctions was the first verification of ASB's view that rapidly tightening global supply would lift prices over 2016.
It was estimated the New Zealand dairy herd had shrunk an unprecedented 5%, or 300,000 cows, on top of the 3% fall last season.
That heavy slaughtering would translate into lower production, with the only question being by how much. New Zealand production data through the spring would be telling.
With the New Zealand supply response more advanced than the EU's, the wedge was expected to widen between New Zealand-dominated products such as whole milk powder and EU-dominated ones such as skim milk powder, he said.