It mostly benefits jobs mainly done by women, including cleaners, carers, clerical workers, school crossing guards and lunch-time staff.
Workers on less than £21,000 a year will also receive an increase higher than any nationally-agreed settlement.
Unison local branch secretary Stephen Smellie said: "The council, and council leader Eddie McAvoy, are to be congratulated on this decision to recognise the need to protect and improve the pay of their low-paid staff."
He said the workers "deliver crucial services to local communities" and had been hit hard by low wages and high prices.
Unison said this is the third year running that the council has made efforts to protect the lowest-paid.
Reps successfully lobbied councillors in 2011 for the living wage and £250 for low-paid staff.
Unison is pressing for council-funded contractors to pay the living wage rather than the minimum £6.19 an hour.