Bobrovsky took a shutout into the third period before allowing a power-play goal to Erik Karlsson with 2:27 remaining.
Fedor Tyutin and Ryan Johansen each provided a goal and an assist while R.J. Umberger and Derek MacKenzie also scored for the Blue Jackets, who improved to 3-4-2 on the road.
Craig Anderson made 18 saves for the Senators, who wrapped up a five-game homestand with a 3-2-0 mark.
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