Conductors and station staff, working with British Transport Police (BTP), had been briefed to inform passengers about how the new by-law would operate, with the aim of raising awareness rather than making arrests.
On-train catering trolleys called last orders at 8.30pm, half-an-hour before the ban – which lasts until 10am – took effect.
The cross-border Caledonian sleeper service is the only one to be exempt from the ban.
The crackdown, aimed at tackling anti-social behaviour, has been welcomed by Scottish Government ministers but provoked a cautious response from rail watchdog Passenger Focus, which warned it could prove unenforceable and lead to thousands of people who are not causing any problems being targeted.
Steve Montgomery, ScotRail's managing director, and Chief Superintendent Ellie Bird, BTP area commander for Scotland, were due to be out with rail staff and police officers last night when the ban came into force.
Ms Bird said she believed it would be widely respected. "It's not just a policing solution, it's about educating people to say it is not acceptable. If you look at the smoking ban, the same thing happened. It became unacceptable to do it," she said.
She said the police response would be "discretionary", based on police resources and the seriousness of an incident.
"We're not going to stop a train if someone is drinking alcohol," she added. "We don't need to increase police resources. It's about being proportionate. The last thing we want to do is to hold all trains while ScotRail wait for the police to arrive."
A spokesman for BTP said he did not expect the number of arrests to increase last night. "The first two weeks will very much be about education and awareness," he said.
A Scottish Government consultation invited views on a blanket ban of alcohol on train services but received a mixed response. Among the 1283 responses received there was a "sizeable number" in favour of a total ban on alcohol consumption but a similar number who supported a more detailed analysis into the link between alcohol and anti-social behaviour.