Nanopores have recently emerged as high-throughput tools for probing and manipulating nucleic acid secondary structure at the single-molecule level. While most studies to date have utilized protein pores embedded in lipid bilayers, solid-state nanopores offer many practical advantages which greatly expand the range of applications in life sciences and biotechnology. Using sub-2 nm solid-state nanopores, we show for the first time that the unzipping kinetics of individual DNA duplexes can be probed by analyzing the dwell-time distributions. We performed high-bandwidth electrical measurements of DNA duplex unzipping as a function of their length, sequence, and temperature. We find that our longer duplexes (>10 bp) follow Arrhenius dependence on temperature, suggesting that unzipping can be approximated as a single-barrier crossing, but the unzipping kinetics of shorter duplexes do not involve a barrier, due to the strong biasing electrical force. Finally, we show that mismatches in the duplex affect unzipping times in a position-sensitive manner. Our results are a crucial step toward sequence variability detection and our single-molecule nanopore sequencing technology, which rely on parallel detection from nanopore arrays.