Friction-induced vibrations affect the performance and service life of mechanical systems and contribute to noise generation. One way to address this issue is to develop anti-friction composite materials with the required tribological properties. This study investigated the effect of TiNi reinforcing particles on the tribological properties of Babbitt-based (SnSb11Cu6) composite materials during friction against a steel counterbody. Babbitt powder (400–500 µm) served as the matrix, while TiNi powder (<100 µm)—produced via the calcium hydride process—served as the reinforcement. This type of reinforcement was chosen for its high wear and corrosion resistance, superelasticity, and high loss tangent, which ensure vibration-damping properties. Composite materials containing 3 wt.% TiNi particles were fabricated using powder metallurgy. Tribological tests on the specimens were conducted under dry sliding friction conditions in an axial loading configuration, with a pin made of the material under investigation sliding against a rotating steel disk. Tests were performed with stepwise axial loading (1, 2, 3, 4, and 5 MPa) at a sliding speed of 0.5 m/s for each load level. Each specimen underwent a sliding distance of 300 m under each axial load, resulting in a total sliding distance of 1500 m. Studies have shown that reinforcing the antifriction matrix with 3 wt.% TiNi particles allows the friction coefficient to remain virtually unchanged while increasing wear resistance by 14.5%. The reduction in vibration and stabilisation of the friction process, attributed to the damping properties of TiNi, are particularly evident in the friction coefficient distribution density maps for the composite specimens at a load of 3 MPa. These results support the recommendation to use TiNi particles in the production of composite materials to enhance the performance of tribological assemblies, reduce vibration, and improve the stability of the friction process.