Thompson cut it to 3-2 with a one-timer from the left circle on the power play at 3:21. Olofsson was left uncovered and tied it 3-3 from the right circle at 6:29 off a fake-shot pass from Power that froze DeSmith.
"Like everyone else, I thought he was going to shoot it at first," Olofsson said. "But I was ready for it. It was a nice fake pass and fake shot and incredible pass."
Tuch drove to the net and redirected a pass from Thompson to give Buffalo a 4-3 lead at 10:34.
"To give up the goal immediately to fall down two goals, we hadn't had a good night to that point yet, and then we responded," Sabres coach Don Granato said. "So, it is a testament to the group's will, determination. But I think they also, they know and we know their identity, and we knew we weren't playing to it to that point. I think the collective feel going into the third (was), 'We are going to get to that, and we are going to turn it up.'"
Kyle Okposo (18:24) and Olofsson (19:53) each scored an empty-net goal for the 6-3 final.
It was the first time the Sabres scored five goals in the third period of a game since a 6-3 win at he Boston Bruins on Dec. 26, 2015.
"[The mood in the room is] what you'd expect for a team that's blown a couple of leads on back-to-back nights and winless in six," Crosby said. "I mean, it's not a great feeling and we've got to find a way to get out of it."