The match was rescheduled to Monday after heavy rainfall on Sunday rendered the pitch unplayable.
The result marked Rivers United’s first defeat of the 2025 Nigeria Premier Football League (NPFL) season.
Shuaibu Garba opened the scoring for Bayelsa United in the 28th minute to give the visitors an early lead.
Chinedu Emmanuel extended their advantage with a second goal 19 minutes from full time.
Rivers United’s Stephan Manyo pulled one back deep into stoppage time, but it was not enough to salvage a point for the hosts.