Werner, who had been linked with a move to Bayern Munich either this year or in 2020, signed a new deal which will keep him at Leipzig until 2023.
“I hope that a lot of people are happy about it,” Werner told broadcasters Sky after the game.
“I didn’t say anything (about the contract negotiations) for a long time, but in the end I decided to stay here.”
“I have always had good experiences in Leipzig, and I feel comfortable.”
The extension was announced shortly before kick-off, and the 23-year-old Germany international promptly proved his worth by opening the scoring with a poacher’s finish.
With just 10 minutes on the clock, Werner hooked the ball in at the far post after Yussuf Poulsen had flicked it on at a corner.
Poulsen appeared to have decided a tense game in the home side’s favour with a sumptuous volley ten minutes from time.
Leipzig, though, had to survive six nervy minutes of injury time after Goncalo Paciencia pulled one back for Frankfurt in the 89th minute.
The win leaves Leipzig in joint second, alongside Borussia Dortmund and Freiburg as one of only three Bundesliga teams who have won both their opening games.