Bank of Scotland's purchasing managers' index, a composite indicator of economic health, hit a seven-month high of 52.3 in January, where a reading above 50 indicates expansion.
This was up from 51.2 in the previous month and was slightly ahead of the UK-wide reading of 52 points.
Meanwhile, there was another rise in employee numbers in Scotland during January, the seventh in the past eight months, but it was modest and slower than the UK average.
Donald MacRae, chief economist at Bank of Scotland, said: "The Scottish economy gained momentum in January this year.
"Both the level of new business and employment rose in the month but were concentrated in the service sector.
"This result suggests the Scottish economy not only started the year in growth mode but has maintained moderate growth throughout January 2013."
There had been hopes that a growth in the manufacturing sector, led by an increase in exports, would reduce the economy's reliance on volatile sectors such as financial services.
But Bank of Scotland found that manufacturing output shrank for the seventh consecutive month in January.
With new orders increasing just fractionally, ending a period of continuous contraction stretching back to April 2012, this was not enough to persuade companies to add workers.
January saw the sixth consecutive month of job losses in the manufacturing sector with the biggest contraction since August last year.
Mr MacRae said: "The rate of decline in manufacturing output was modest and has eased since the previous month but export demand remains weak."
There was improved underlying domestic demand for manufactured goods while the amount of new work coming from overseas fell after a brief pick-up in December.
But Bank of Scotland highlighted that this fall was only marginal and much weaker than during the previous six-month stretch of decline.
Scotland's dominant service sector continues to expand, growing at a slightly accelerated rate in January to mark the 25th consecutive month of expansion.
The increase was the sharpest since April last year. But it was coupled with a rise in employee numbers, which although its most significant since August, remained at a modest level.
This uncertain picture of the economy was matched by separate analysis by accountant BDO.
Its UK-wide research found both falling optimism among businesses and declining output, suggesting the economy could struggle to grow in the current quarter, leading to a triple-dip recession.
Yet, its employment index, which measures businesses' hiring intentions over the next two quarters, suggested a degree of business confidence after indicating expansion in jobs for the first time since April.
Neil Craig, head of BDO in Scotland, said: "In spite of a strengthening labour market, business confidence continues to weaken, and improved hiring intentions are not translating into growth plans.
"It seems the damaging effects on businesses of five years' zig-zagging economic growth has left them wary of making concrete plans for expansion and resigned to the 'new normal' of economic stagnation.
"To end this cycle, it is imperative the Government implements plans to expedite growth.
"Without growth incentives, we will continue to see UK businesses reluctant to invest and expand, which poses a grave threat to the UK's economic recovery."