Experts now say predictions the market would cool were premature, as investors found ways to circumvent controls.
The city's median price was up from $720,000 in January and $750,000 in February, according to Real Estate Institute data.
North Shore median prices rose in March to $1 million, from $940,000, and Auckland City prices jumped to $962,000, from $825,000.
"Recent fears of the Auckland market cooling have been overstated, as median prices across the city have rebounded during March," institute chief executive Colleen Milne said. "The slowdown in sales volumes after the introduction of tax and LVR changes last year appears to be coming to an end."
Elsewhere in New Zealand, price also rose. Otago, Northland, Manawatu/Wanganui, Wellington and Waikato/Bay of Plenty all showed in excess of 25 per cent annual sales growth, REINZ said. The national median house price rose $20,000 or up 4.2 per cent to $495,000 annually.
In Auckland, the LVR changes demanded investors stump up 30 per cent deposits. Everyone else needs to raise 20 per cent. A capital gains tax of sorts was introduced for those hocking off fast-appreciating investment properties within two years.
The market's rise from its summertime slumber comes as no surprise to economist Shamubeel Eaqub.
"This is when you would expect to see the new regulations being tested," he said last night.
"It will be around six months for these new regulations to work through the system. That's what we saw with the first-home buyer restrictions put in place a little while ago."
People were learning how to work around the restrictions, he said.
Labour Party housing spokesman Phil Twyford said Government measures to cool Auckland's market had not gone far enough. "The $70,000 increase in one month is almost one-and-a-half times the median income in Auckland," he said.
National needed to take "meaningful action" and "embark on a massive state-backed building programme to flood the market with affordable homes", Mr Twyford said.
He also called for planning-rule tweaks and a ban on overseas speculators.
Building and Housing Minister Nick Smith said figures for Auckland had been volatile recently. Ideally, the government would like to see year-on-year growth in the single figures for percentage points, as was the case earlier this year.
"I'm hesitant to draw conclusions on the basis of just one month's data," Dr Smith said. "It's certainly clear that there was much softening in the latter part of 2015."
The minister said he hadn't seen any evidence to suggest buyers were finding ways to work around measures introduced last year.
The comments come as Auckland Council revealed it received a record 23,220 consent applications, up by 12 per cent.
Most property in Auckland is being picked up by "multiple property owners". CoreLogic data issued by QV shows that sector accounted for 44 per cent of all sales. First-home buyers were involved in 21 per cent of purchases.
Investors were seeing good returns, said QV Auckland spokesman James Wilson. "Historically, Auckland's been able to provide that."
Lower- and mid-price houses were experiencing growth and there was interest in Manukau and Papakura, where investors and first-home buyers were effectively competing.
Meanwhile, the institute revealed that one in three properties in Auckland went for more than $1 million last month.
Mr Wilson said it was simply "a numbers game".
"When the market keeps moving the way it's moving, you're going to get to a point where areas get tracking over $1 million."
The institute said Waikato, Bay of Plenty, Wellington, Nelson, Marlborough, Canterbury and Westland were also experiencing record median prices, in what it called Auckland's "halo effect".
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