Mr Mackay unveiled his draft budget last month, including plans for an overhaul of the tax system which leave higher earners paying more than counterparts elsewhere in the UK. Lower earners would get a small cut.
But the Greens have already demanded an extra £150 million for councils to ensure vital frontline services don’t suffer.
Patrick Harvie’s amendment called for the budget changes to “protect public services, fund a fair pay increase for public sector workers and invest in low-carbon infrastructure.”
It was passed by 67 votes to 56, as Greens and SNP MSPs out-voted the other opposition parties.
Mr Harvie said: “For months, Greens have been focused on reversing cuts to council budgets, achieving a fair pay increase for frontline workers, and increasing the proportion of capital spend on low-carbon infrastructure.
“Greens have shifted the debate on tax to show that revenue can be raised while protecting low and middle earners.”