Werner repeats double trick as Leipzig goes 3rd in Germany
If Werner scores, he often adds another. It was the fourth league game in which the Germany striker claimed two goals, bringing his tally to eight so far this season.
Alassane Plea and Raffael went close in the second half for the visitors.
The result leaves Bundesliga leader Borussia Dortmund seven points clear after the 13th round.
Daniel Ginczek scored one goal and set up another for Wolfsburg to beat Frankfurt 2-1 and stop the home side from moving second.
Frankfurt could have moved ahead of Gladbach on goal difference, but Ginczek set up Admir Mehmedi in the first half and then scored the second.
Frankfurt had a goal ruled out for offside and several good chances before Luka Jovic finally scored in the 87th.
Frankfurt is fifth, a point behind Bayern Munich, while Wolfsburg climbed to eighth with its second successive win.