The strong winds also hampered efforts to restore power.
People were advised to treat all downed lines as live and report them to Vector.
The low pressure system is expected to continue to bring wet weather to most of the North Island this week.
MetService has issued a severe weather warning for the central and upper North Island, for heavy rain and the possibility of severe west to northwest gales.
Aucklanders in particular battled downpours and strong winds yesterday.
MetService reported winds gusting 150km/h at Manukau Heads and 85km/h on the harbour bridge.
In West Auckland, trampolines were sent flying and trees were torn from the ground.
A Northern Fire Service spokesman said West Auckland had "really got the brunt" of the westerly winds. Firefighterswere called out to around half a dozen weather-related incidents, including two call-outs to retrieve trampolines stuck on roofs.
About 1200 houses were without power in Greenhithe yesterday morning and around 500 houses were affected in Coatesville.
About 900 houses in Titirangi were also without power - the outage caused by a tree that fell on a power line.
Power was restored to most areas by the afternoon.
Isolated showers should give way to fine weather in Auckland today, but periods of heavy rain are possible tomorrow with a northeasterly wind developing. A high of 17C is expected.
In Tauranga, rain is forecast to clear this afternoon, while in Whangarei, westerlies are set to die out. Periods of rain, possibly heavy, are forecast for both regions tomorrow.
In Hamilton showers are expected to clear this evening, while rain and easterlies develop tomorrow morning with a high of 14C forecast.
Forecast
Whangarei: Cloudy with westerlies dying out. Periods of rain, possibly heavy, tomorrow with winds turning northwest.
Auckland: Fine spells expected with isolated showers clearing in the afternoon. Periods of rain expected tomorrow, with heavy falls possible.
Hamilton: Showers expected, clearing in the evening. Tomorrow rain develops in the morning.
Tauranga: Rain forecast but clearing in the afternoon. Rain, possibly heavy, predicted for tomorrow.
Wellington: Cloudy with a few showers that should clear in the afternoon. Tomorrow high cloud increases, with rain forecast in the afternoon.
