Opposition parties supported the changes - but were critical an alcohol law passed in 2012 had meant the Returned and Services Association faced an expensive licensing process.
The member's bill was put up by National MP Paul Foster-Bell at the request of the RSA, and amends legislation which requires RSAs to get a special licence, costing about $500 each year, to serve alcohol before midday on April 25.
Mr Foster-Bell has said that affected the traditional "gunfire breakfasts"- an Anzac Day tradition since the 1920s.
Adding a shot of rum to coffee at breakfast recalled the repast taken by soldiers prior to battle and the rum ration was standard military issue of that time.
Parliament's business committee determined that the bill would progress through all stages this afternoon, and there would be no debate on the second reading, enabling the law to be changed in time for this year's Anzac Day.
Mr Foster-Bell said it would act as an "ideal 100th birthday present for the RSA".
"It is a nice birthday present and, of course, it is then in place forever. Unlike the Rugby World Cup alcohol changes, this doesn't have a sunset clause."
He was pleased that the change had the support of all parties, and said Labour MP Kris Faafoi had been particularly helpful.
"It is one of those rare things that seems to have unanimous support across the whole House. That doesn't happen very often, and that's what allowed this to be fast-tracked.
"Under the usual process it might have gone for months potentially, and it wouldn't have been done anywhere near in time for this year."
Green Party health spokesman Kevin Hague said his party - which took issue with Act leader David Seymour's successful push to allow bars to open for Rugby World Cup games - had no concerns about the RSA change.
"What Paul Foster-Bell's bill does is really just for a very, very small cross-section of licensed premises, and only for one day of the year. So it is a very minor extension.
"And I think absolutely nobody begrudges those old soldiers the opportunity for a drink once a year."
Mr Hague said the fast-tracked process was far from ideal, and was critical that the problem had not been picked up when the Sale and Supply of Alcohol Act 2012 was passed under former Justice Minister Judith Collins.
Labour and NZ First were also critical that the 2012 legislation had missed the problem.
Current Justice Minister Amy Adams said there were no major flaws in the act.
"This [issue] with the RSAs, I looked at the issue and thought, actually, we do want RSAs to be open on Anzac morning.
"That is their biggest day of the year, and it makes sense to me."
