British Transport Police (BTP) says it dealt with only four incidents related to a specific alcohol railway byelaw throughout 2013.
In July 2012, First ScotRail banned the consumption and carrying of alcohol between 9pm and 10am.
ScotRail also refuses travel to those who are not considered fit to do so due to the effects of alcohol.
From that date until end December 2012 there were nine reported incidents with six people reported to the procurator fiscal.
Jacqueline Taggart, customer services director at ScotRail, said: "This is welcome news and demonstrates that the vast majority of rail passengers respect, and welcome, the ban.
"I would like to thank people for their co-operation in this regard.
"We remain committed to working with BTP to support our customers and staff in this important area.
"This is an important year for Scotland and, as a major transport operator, we take our contribution very seriously."
In 2013, there were even fewer incidents, with three people being reported to the procurator fiscal.
They included an 18-year-old man who was caught drinking on a Glasgow Central to Ayr service travelling in the Kilwinning area at 10.20pm on April 26 and an 18-year-old woman was in possession of alcohol and who was drunk at Queen Street Station at 10.35pm on September 1.
Superintendent John McBride from the BTP said: "The message that anti-social behaviour at stations and on trains is unacceptable is clearly being heeded by those who use the rail network.
"We will continue to support ScotRail in ensuring everyone can travel and work without encountering unwelcome or unwarranted disorderly behaviour."
John Mason MSP, convener of the Cross Party Group on Rail in the Scottish Parliament, added: "Of course there are still problems but we are going in the right direction."