Eichel had a goal and two assists, and Rasmus Dahlin had two assists for the Sabres (26-24-8). Carter Hutton made 28 saves.
Columbus, which is tied with the Philadelphia Flyers for the first wild card into the Stanley Cup Playoffs from the Eastern Conference, is 0-1-2 in its past three. The Blue Jackets and Flyers are also one point behind the New York Islanders for third in the Metropolitan Division.
Gerbe one-timed a Vladislav Gavrikov pass in the slot to put the Blue Jackets up 1-0 with 28 seconds left in the first period.
Boone Jenner deflected Zach Werenski's point shot to make it 2-0 at 1:31 of the second period.
Eichel cut it to 2-1 at 18:47 with a wrist shot from the top of the left circle.
"In that situation, we need to end that period being up 2-0," Blue Jackets coach John Tortorella said. "Three of our veteran forwards get caught, give up a 3-on-2 from their goal line, [the puck is in the] back of the net. … That's the hard part for me, just the situational play of some players. Glad we found a way to get a point. Had some chances in overtime. They did too. We lose."