DNA-based data storage is an emerging nonvolatile memory technology of potentially unprecedented density, durability, and replication efficiency. The basic system implementation steps include synthesizing DNA strings that contain user information and subsequently reading them via high-throughput sequencing technologies. All existing architectures enable reading and writing, while some also allow for editing and elementary sequencing error correction. However, none of the current architectures offers error-free and random-access readouts from a portable device. Here we show through experimental and theoretical verification that such a platform may be easily implemented in practice using MinION sequencers. The gist of the approach is to design an integrated pipeline that encodes data to avoid synthesis and sequencing errors, enables random access through addressing, and leverages efficient portable nanopore sequencing via new anchored iterative alignment and insertion/deletion error-correcting codes. Our work represents the only known random access DNA-based data storage system that uses error-prone MinION sequencers and produces error-free readouts with the highest reported information rate and density.