Germany international Werner, who had also scored in their league opener last week, signed a contract extension until 2023 before the game on Sunday and then fired in at the far post.
Shortly before the start of the game, the club announced the new deal with Werner, who had been repeatedly linked with a move to Bayern Munich in the past months.
The 23-year-old, who had scored 62 goals in 116 matches for the club prior to Sunday, delivered again after just 10 minutes.
Poulsen added their second with a sizzling volley in the 80th minute before Frankfurt pulled a goal back with Goncalo Paciencia’s close-range tap-in a minute from the end.
Champions Bayern Munich beat Schalke 04 3-0 thanks to a Robert Lewandowski hat-trick on Saturday that lifted them to four points from two matches. (Reporting by Karolos Grohmann Editing by Ian Chadband)