A technique provides data storage system services in data storage equipment. The technique involves performing, by processing circuitry of the data storage equipment, data storage operations on a production volume in response to data storage commands from a set of application servers (e.g., external host computers). The production volume stores application server data utilized by the set of application servers. The technique further involves running, by the processing circuitry of the data storage equipment, an instance of a virtual backup appliance within the data storage equipment while the data storage operations are performed on the production volume in response to the data storage commands. The technique further involves generating, by the processing circuitry of the data storage equipment, backups of the production volume via the instance of the virtual backup appliance running within the data storage equipment.