The woman grabbed it and tried to hold on. She struggled with the thief until the strap broke and he took off.
As he ran, the 66-year-old tried to stop him. The man pushed her to the ground, causing her to bang her head.
She was knocked out briefly, but did not suffer serious injuries and was recovering in Middlemore Hospital.
The thief got into a stolen silver Mazda, registration DGQ299, and drove off.
Police were appealing for witnesses to contact them.
In August police issued a warning specific to Asian women - who were said to be targeted most often by bag snatchers.
Detective Wong Woo said there had been a "disturbing trend" of similar incidents at the time.
Mr Woo said police were working hard within Asian communities to get important safety messages across.
"Education programmes within these communities have helped hugely to get the message across not to carry large amounts of cash or jewellery and not to write down Pin numbers."
Mrs Wang was run down by men in a stolen 4WD in the carpark of the Manukau Westfield shopping centre.
Her young son witnessed the horrific incident from the van his mother had been getting into.
Christopher Shadrock was found guilty of Mrs Wang's murder and sentenced to life in prison. Four other men were found guilty of being accessories.