A system includes a host processor, which has a host memory and is coupled to store data in a non-volatile memory in accordance with a storage protocol. A network interface controller (NIC) receives data packets conveyed over a packet communication network from peer computers containing, in payloads of the data packets, data records that encode data in accordance with the storage protocol for storage in the non-volatile memory. The NIC processes the data records in the data packets that are received in order in each flow from a peer computer and extracts and writes the data to the host memory, and when a data packet arrives out of order, writes the data packet to the host memory without extracting the data and processes the data packets in the flow so as to recover context information for use in processing the data records in subsequent data packets in the flow.