Direct response to IO request in storage system having an intermediary target apparatus

An apparatus comprises at least one processing device comprising a processor coupled to memory. The at least one processing device is configured to obtain an input-output request issued by an application executing on a compute node via at least one network and to identify a storage node as corresponding to the obtained input-output request based at least in part on the obtained input-output request. The at least one processing device is configured to associate information corresponding to the compute node with the input-output request and to submit the input-output request and the associated information that corresponds to the compute node to the storage node via the at least one network. The storage node is configured to submit a response to the input-output request to the compute node via the at least one network based at least in part on the information.