Greaves also made 24 saves in a 4-2 win versus the New York Islanders on Sunday.
Damon Severson had a goal and an assist, while Cole Sillinger and Charlie Coyle each had two assists for the Blue Jackets (17-15-6), who won their third in a row.
Tim Stutzle extended his point streak to 10 games with an assist, Jake Sanderson scored and Leevi Merilainen made 18 saves for the Senators (18-15-5), who have lost three straight (0-2-1) after a four-game winning streak.
The NHL had to push the game’s start time back 30 minutes to 7:30 p.m. ET due to the Blue Jackets’ late arrival. The team’s flight on Sunday was canceled due to mechanical issues, and Monday’s inclement weather resulted in Columbus finally touching down in Ottawa at around 3:50 p.m. ET.
Ottawa was 0-for-4 on the power play, while Columbus was 0-for-3.
Boone Jenner redirected a centering pass from Sillinger over Merilainen’s left pad to give the Blue Jackets a 1-0 lead at 15:58 of the first period.
Severson one-timed a pass from forward Dmitri Voronkov past Merilainen’s blocker on the rush to push it to 2-0 at 1:21 of the second period.
Sanderson cut it to 2-1 at 8:16. Stutzle found Sanderson streaking down the left side and the defenseman beat Greaves under the left pad with a wrist shot from the top of the left face-off circle. Stutzle has eight goals and nine assists in his 10-game point streak.
Denton Mateychuk’s snap shot from the point beat Merilainen glove side to extend Columbus’ lead to 3-1 at 1:57 of the third period.
Kirill Marchenko scored with a curl-and-drag snap shot into the top left corner on a rush to make it 4-1 at 15:54.