Ville Leino opened the scoring with a goal at 4:58 of the second period when he beat Columbus goaltender Mike McKenna.
Buffalo made it 2-0 at 9:10 of the third when Grigorenko beat Columbus goalie Jeremy Smith over the right shoulder.
Grigorenko assisted on Zemgus Girgensons' empty-net goal in the final minute.
Sabres defenseman Mike Weber had assists on all three goals.
Columbus hosts the Carolina Hurricanes on Thursday to end the preseason while the Sabres host the Hurricanes on Friday in Carolina.
- Ice Hockey
- Sports & Recreation
- Buffalo Sabres
- Columbus Blue Jackets
- Mikhail Grigorenko