Colten Ellis made 27 saves in his NHL debut for the Sabres (3-4-0), who have won three of four. Jason Zucker and Josh Doan also scored, and Ryan McLeod and Conor Timmins each had two assists.
Buffalo acquired Ellis off waivers from the St. Louis Blues on Oct. 6.
J.T. Compher and Emmitt Finnie scored for the Red Wings (5-2-0), who had not lost since their season opener against the Montreal Canadiens on Oct. 9, 5-1. John Gibson made 27 saves.
Compher gave Detroit a 1-0 lead at 3:00 of the second period. Albert Johansson put a shot on net from the left circle, drawing Ellis over, and Compher was in front to collect it and push it into the net.
Zucker tied it 1-1 at 11:37 when he took a pass from Quinn at the top of the crease on a 2-on-1 rush and scored on Gibson stick side.
Zucker left the game with an upper-body injury at 14:22 and did not return.
Tyson Kozak gave Buffalo a 2-1 lead at 16:28. Quinn cut to the slot from the right side before sending a short pass to Kozak in front, where he slid it through Gibson’s pads.
Finnie tied it 2-2 at 18:20 after Dylan Larkin sent him a backhand feed from below the right circle for the quick tap-in.
Quinn put Buffalo back ahead 3-2 on the power play at 4:15 of the third period when he one-timed a pass from McLeod from above the slot.
Doan then extended it to 4-2 at 8:10, scoring on a one-timer from the top of the left circle.