Werner created the chance for Olivier Giroud to open the scoring on 31 minutes, before the Germany international tapped home from close range in the 39th minute.
The win continues Chelsea’s excellent form under new boss Thomas Tuchel, rising above Liverpool into fourth spot, while Newcastle are now one spot above the drop zone.
West Ham United knocked off Sheffield United 3-0 earlier on Monday, meaning the Hammers are also above the reigning champions who drop to sixth.
But Werner’s drought-breaking goal was worthy attention, having not netted in the Premier League since mid-November.
“Yes of course, as a striker you always want to score,” Werner said post-game.
“The last month was so good. I was happy without scoring but when we win everything is good. When I help my team with assists and now scoring I’m happy. I’m very glad I scored today.
“I’ve had in the past a lot of chances and I missed them. Today the team brought me into situations to score. When I keep going, the goals will come like today.”
Meanwhile, Declan Rice, Issa Diop and Ryan Fredericks all scored as West Ham swept aside bottom club Sheffield United to rise to fifth.
Hammers boss David Moyes said: “Were a team in progress, were trying to grow, were trying to get good foundations in place so that maybe in the future we can have regular good teams at the top of the league.
“So, were enjoying it at the moment why would we not enjoy being in the position were in? and I just want the players to keep improving.”