Speaking before the third reading, Twyford said new standards might see extra costs for landlords.
"We think between $3000 and $5000, if you have to insulate from scratch and put in a heat pump. But we're going to be providing grants of up to $2000 per property to assist with that."
He said the winter fuel payments of $140 a week that the Government plans to introduce next year for older and low-income families will also help.
"We can't afford not to act. For every dollar you spend on retrofitting, you save $5 to $6 in public health spending. It's just time for us to do the right thing."
He did not think the bill's minimum standards would push up the price of renting.
"We think it will be pretty marginal, if at all. Rents are set by supply and demand, and if all of the landlords in the market have to meet these standards, one can't compete against the other by undercutting them by not providing those standards."
The National Party has criticised the bill as meaningless, saying that legal minimum requirements were already in place.
The Government will run a consultation process over the next 18 months to ensure that tenants, landlords, public health and building science experts and industry representatives have an opportunity to get involved in creating robust minimum standards.
Green Party housing spokeswoman Marama Davidson said the passing of the bill would have a positive impact on hundreds of thousands of families.
"The Healthy Homes Guarantee Bill will significantly improve the quality of rental accommodation, lifting children out of poverty and helping to reduce deaths from preventable diseases."