Scottish Ambulance Service control centres answered 2878 calls between 7pm on Monday and 7am yesterday – an increase on the previous year's figure of 2666. The service said the busiest period was between midnight and 4am.
The total was just short of the busiest New Year on record – when 3141 calls were made to the service's three emergency centres two years ago.
The increase is almost entirely because of a large spike in calls to control centres in the west of Scotland – including Glasgow –where the total soared by about one-third from 1090 to 1303.
In the east of Scotland the number of emergency calls rose to 1090 from 1088 and in the north there was a drop from 488 to 485.
Extra staff – including call handlers, dispatchers and ambulance crews – had been brought in for what is traditionally seen as the ambulance service's busiest night of the year.
Daren Mochrie, of the Scottish Ambulance Service, said: "Our staff showed their professionalism and commitment on what is the most challenging night of the year, and did a fantastic job. They worked through the night to respond to patients in need, when demand is at times extremely intense."
New Year's Day events took place yesterday as the clean-up continued after the Hogmanay revels.
Around 300 people took part in the New Year's Day triathlon in Edinburgh, where competitors swam 400m at the Royal Commonwealth Pool, cycled 11 miles around Arthur's Seat and ran 3.5 miles.
There was also a huge street theatre event in the south side of the capital last night.
It was estimated 75,000 people had gathered in Edinburgh for the world-famous Hogmanay celebrations to hail in 2013.
Lothian and Borders Police praised the crowds, revealing there were only four arrests over the course of the night.
The Hogmanay celebrations featured the Concert in the Gardens with performances by Scottish rock band Simple Minds, The View and Bwani Junction.
It was hailed a success by police and by Edinburgh councillor Steve Cardownie, who described the event as "truly fantastic".
There were fireworks displays throughout the evening, culminating in a spectacular show at the castle at midnight.
After the celebrations, work began to clear the tonnes of rubbish left behind and to remove stages, safety barriers, scaffolding and screens.
Pete Irvine, artistic director of Edinburgh's Hogmanay, said: "I think what is happening here is we are pretty well established, we are the best party on the planet and people are here from all over the world."
The three days of new year celebrations in Edinburgh is worth about £32 million to the Scottish economy, with around 150,000 tourists attracted to the capital.
Elsewhere, a sell-out crowd of more than 20,000 people congregated in Stonehaven's historic Market Square to welcome in the new year. Other Hogmanay events included a concert at Stirling Castle, headlined by The Proclaimers; the Red Hot Highland Fling in Inverness with Big Country; and a record 35,000 crowd celebrating Hogmanay in Shetland.
There were, however, no official celebrations to bring in the bells in Glasgow for the second year in succession. The city's Hogmanay day event in George Square ended two hours before midnight.