Victor Antipin and Taylor Fedun each had an assist for Buffalo, which handed the Red Wings their fifth defeat in a row.
The win was the first at home for rookie coach Phil Housley and ended the Sabres' three-game home losing streak. Buffalo won consecutive games for the first time this season and improved to 3-5-2.
Pouliot scored with 10:15 remaining in the second period when he took the rebound of Antipin's shot and stuffed a wraparound behind goalie Jimmy Howard. Antipin's assist was the first point of his career.
Pouliot also was a star in the Sabres' 4-3 comeback win in overtime against Boston on Saturday night.
With just more than three minutes left in the second, Lehner denied Red Wings forward Martin Frk with a left pad save on a 2-on-1 chance. Lehner's shutout was the Sabres' first of the season and his first since last February when he stopped 37 shots against Ottawa.
Buffalo continued to struggle on the power play, going 0 for 4 to drop to 5-38 with the man advantage this season. Two of those power plays ended when the Sabres took penalties of their own.
Prior to Tuesday night, the Sabres had never beaten Howard in regulation. The veteran goalie still has never allowed more than two goals in regulation against the Sabres despite falling to 8-1-1 vs. Buffalo in his career.
NOTES: Detroit had three five-game losing streaks last season. ... Sabres center Jordan Nolan played in his 300th NHL game. ... Sabres forward Zemgus Girgensons and defenseman Justin Falk both skated with the team for the first time since getting injured Oct. 5. Both are day to day, according to Housley. ... Howard has permitted four goals in his last three games against the Sabres, including one-goal efforts in his past two trips to Buffalo. ... Red Wings forward Dylan Larkin was held without a goal for the ninth straight game. He has just one goal this season after combining for 40 in the previous two seasons.
Red Wings: At the Tampa Bay Lightning on Thursday night in the second of a three-game road trip.
Sabres: At the Columbus Blue Jackets on Wednesday night.