Polybutene-1 with form I crystals exhibits excellent creep resistance and environmental stress crack resistance. The filaments of polybutene-1 and its random copolymer with 4 mol% ethylene co-units were produced via extrusion melt spinning, which are expected to be in form I states and show outstanding mechanical properties. The variances in microstructure, crystallization–melting behavior, and mechanical properties between homopolymer and copolymer filaments were analyzed using SEM, SAXS/WAXD, DSC, and tensile tests. The crystallization of form II and subsequent phase transition into form I finished after the melt-spinning process in the copolymer sample while small amounts of form II crystals remained in homopolymer filaments. Surprisingly, copolymer filaments exhibited higher tensile strength and Young’s modulus than homopolymer filaments, while the homopolymer films showed better mechanical properties than copolymer films. The high degree of orientation and long fibrous crystals play a critical role in the superior properties of copolymer filaments. The results indicate that the existence of ethylene increases the chain flexibility and benefits the formation of intercrystalline links during spinning, which contributes to an enhancement of mechanical properties. The structure–property correlation of melt-spun PB-1 filaments provides a reference for the development of polymer fibers with excellent creep resistance.