However, supply bottlenecks, material shortages, rising energy prices and Russia’s invasion of Ukraine also led to record increases in costs and prices, according to the latest Royal Bank of Scotland (RBS) PMI report.
Manufacturing output also fell for the third time in four months with factories suffering faster cost inflation than services firms.
Overall, the report’s seasonally adjusted activity index posted a reading of 58.4 in March, rising from February's 55.5.
Firms saw the sharpest uplift in new orders in four months, driven solely by the service sector as new manufacturing orders fell.
Optimism about the year ahead remained strong in March across Scotland and registered above the long-run survey average on the back of the continuing recovery from the pandemic. However, sentiment has weakened since February and was softer compared to the UK as a whole.
In terms of employment, firms registered a twelfth straight rise in workforce numbers during the month. Staffing levels increased amid growing workload pressures and in preparation for a rise in business needs in the months ahead, according to the survey of firms.
Last week, separate figures from RBS showed that Scottish recruitment activity was continuing to rise sharply despite labour shortages. Permanent placements increased at the second-fastest rate on record as recruiters across Scotland saw another "robust" uplift in hiring activity.
Cost pressures faced by Scottish private sector companies remained steep in March, with the overall rate of input price inflation reaching a fresh record high.
However, the rate of input price inflation in Scotland was marginally slower in comparison to the UK average.
Malcolm Buchanan, chair of RBS’s Scotland board, said the overall figures reflected improving confidence levels as the pandemic recovery continues.
“Crucially, however, trends diverged by sector as sharp growth in output at services firms managed to offset a slight contraction in manufacturing production,” he said.
“Given the current state of play with regards to inflation, the downside risks to the demand-side of the economy have intensified. But it was encouraging to see strong business sentiment, with firms optimistic for growth opportunities if the Covid-19 recovery continues.”