The SNP-led administration's budget was approved by 33 votes to 32 following two hours of debate.
Co-leader Richard Thomson told members he wants to use an extra £6m announced in the Scottish government's budget on a scheme to ease the impact of business rates rises.
The 2.5% council tax increase adds more than £28 to a Band D property.
Higher band properties will see their charges rise more due to national changes agreed last year.
Aberdeenshire councillors have narrowly voted in favour of a 2.5% rise in council tax.