Kreider tied it 1-1 at 19:37, scoring a power-play goal off a pass from Panarin in the slot.
Vinnie Hinostroza made it 2-1 at 2:26 of the second period, stealing the puck from defenseman Jarred Tinordi in the Rangers' zone before breaking in and scoring top shelf.
Jacob Trouba tied it 2-2 at 8:03 on a delayed penalty, poking in a loose puck at the left side of the net.
"We talked about getting more pucks to the net from the blue line," Trouba said. "At the end of the day, you've got to get pucks there and that's kind of how they all end up going in. … You've got to get bodies there and get traffic."
Kaapo Kakko gave New York a 3-2 lead at 12:07, using his time and space to skate from the top of the right circle to the slot before shooting past Dell.
Thompson answered right back at 12:57 to tie it 3-3, and 15 seconds later, Dahlin put the Sabres back ahead 4-3 with a slap shot from the blue line.
K'Andre Miller then responded for the Rangers 17 seconds later to tie it again 4-4, scoring with a point shot through traffic.
"A lot of fun for the people in the building, I'm sure," Granato said. "And again, it's momentum swings. You're in somebody else's building, the crowd is a big part of that four goals. … The noise and the atmosphere and emotion creates and adds to that. That's something we have to manage, but I thought for the most part we showed marked improvement."
NOTES:Lindgren is the 24th player, and fourth defenseman, in NHL history to score a go-ahead goal in the final second in regulation. He is also the fourth player in Rangers history to do so, joining Brad Richards (Dec. 17, 2011), Dean Prentice (Nov. 16, 1960) and Grant Warwick (March 18, 1945). … Victor Olofsson had one assist and one shot on goal in 16:45 of ice time in his first game since Oct. 31. He missed the previous eight games with an undisclosed injury. … Rangers forward Ryan Reaves played in his 700th NHL game.