In response to issues such as the high requirements for uniform seeding and the lack of suitable sowing machinery when using narrow-row dense planting agronomy for small-seed vegetables like spinach, a narrow-row precision seeder that integrated functions such as rotary tilling, ridging, furrowing, seeding, and soil covering was designed. This seeder achieved precise sowing in narrow rows on ridges for densely planted vegetables like spinach. The study outlined the overall design of the seeder, with a focus on the design of the furrowing and seed dispensing assembly. By analyzing the forces and movement of seeds during the dispensing process in a pneumatic needle-type planetary gear system for narrow-row multi-row parallel precision seeding, the main factors affecting seed drop trajectory and plant spacing uniformity were identified. A mechanical model of the furrow opener’s interaction with the soil was constructed, and the structural parameters of the furrow opener disc, sliding knife-type soil separator, and seed drop opening were determined. A discrete element simulation analysis of the furrow opener’s operation was conducted, using furrow depth, sliding knife-type soil separator inclination, and operating speed as test factors, with soil disturbance and furrow depth coefficient of variation as test indicators. A second-order regression orthogonal combination experiment was carried out to determine the optimal parameter combination for the furrow opener as a furrow depth of 45.45 mm, a sliding knife-type soil separator inclination of 20.14°, and an operating speed of 0.40 m/s. Field furrow opening tests showed that under the optimal parameter combination, the coefficient of variation in furrow depth for the disc-sliding knife combination furrow opener was 9.57%, with a soil disturbance amount of 13.37 cm2, indicating superior furrow opening performance. Field seeding tests showed that the coefficients of variation for the number of seedlings per row and consistency of seedlings across rows after sowing with the narrow-row precision seeder were no more than 9.95%, meeting the agronomic requirements for narrow-row dense planting of small-seed vegetables.