Although polydopamine (PDA)-related modification is widely studied in the fabrication of superhydrophobic sponges, the high cost of dopamine limits its widespread application. To imitate PDA modification, a low-cost and facile one-step poly(phenol-amine) modification was performed on melamine sponges in this study. Low-cost catechol and diethylenetriamine (DETA) were used as the monomers, and n-dodecanethiol was used as an additive in the one-step modification. The results confirmed that the poly(phenol-amine) aggregations were successfully anchored on the sponge skeleton surface and that the aggregations were formed via the Schiff base reaction and the Michael addition reaction. Furthermore, the as-prepared sponges still showed excellent mechanical properties after modification. Additionally, the optimally modified sponge (MS-0.5) exhibited superhydrophobic properties with a contact angle value above 150° under various environments, high oil-absorption capacity for various oils and organic solvents, high continuous oil–water separation performance with efficiency greater than 98.8% in 30 cycles, outstanding demulsification performance with 99.52% toward oil-in-water emulsion, and excellent recoverability and long-term stability. Thus, this work provides a feasible facile one-step modification method that can be used in place of PDA-related modification.