A single-storey extension and a detached garage/workshop will be built at Woodburn Drive in Chapeltown.
Seventy local residents, Angela Smith MP, Coun Steve Wilson and Ecclesfield Parish Council had complained, saying the the workshop was an overdevelopment.
Neighbours said a new access point would create problems for emergency vehicles, exacerbate existing parking issues and put pedestrians at risk.
Council officers said the workshop would not be overbearing and was far enough away from all neighbouring properties.
They added that the access would have adequate visibility and wouldn’t put pedestrians at risk.
The planning board agreed and approved the plans.