The hike - comprising 1.4 per cent for core services such as roads and bin collections and a further 1.5 per cent ringfenced for adult social care - could have been as high as 5 per cent.
However, the council said such an increase would further squeeze hardest-hit residents’ finances and leaders went against imposing the highest-possible hike.
An amended budget proposal put forward by the Liberal Democrats - featuring more money for road safety measures, investment in youth services and an improved warden response during snowy conditions - was voted down.
The council tax rise translates to an annual increase of £24.83 for band A homes and £89.40 for band H properties.
Cabinet spokesman for core services, Coun Alan Gardiner, said: “This time last year I set the budget with optimism as it was the first time in years we could invest significantly in our key priorities.
“However, no-one could have predicted the pandemic, but the response by this council has been second to none.
“Millions of pounds have gone towards helping our businesses through it, free school meals have been provided and those most vulnerable have been protected despite challenging circumstances.
“The pandemic’s cost to the council has been more than £12m but given our history of good financial management, we’re still able to deliver a balanced budget.
“A rise of 5 per cent rise has been considered by many neighbouring councils and although major uncertainties are ahead, the 2.9 per cent figure will help us recover and build a better Barnsley.”
The majority of the local authority’s near-£200m ‘core’ funding for the coming year will come from council tax - predicted to be £106.7m - with the rest made up of business rates and government grants.
However, future uncertainty forced by the pandemic has not stopped the authority from committing to wide-ranging investment, listing more than £400m in projects.
Council leader Sir Steve Houghton described the overall budget as a ‘miracle’.
“Most councils aren’t in a sound financial position, but we are and it’s important to keep Barnsley moving through this pandemic,” he added.
“This overall budget is a miracle, as it commits to making investments for the borough’s future at a time when many councils are raising tax to 5 per cent due to the costs they’ve incurred.
“It’s an amazing feat by all involved.”