Mr Dunne's single vote will ensure David Clark's bill to Monday-ise Anzac Day and Waitangi Day, and Ms Moroney's bill to increase paid parental leave to 26 weeks will go to select committees.
Last month Mr Dunne used the same casting vote to back for National's state assets sale plan.
Mr Dunne is in a support agreement with National but that obliges him to support it only in matters of confidence and supply.
National cannot pass a law with the support of Act's John Banks alone, so if the Maori Party does not support an issue Mr Dunne's vote is required.
Mr Dunne admitted he was tempted to withhold support for the Labour MPs' bills in revenge for the "smears" he was subjected to during debate on the state assets sale bill, but decided sticking to his principles was more noble than political utu.
