The German international striker was at his clinical best as Julian Nagelsmann's fine start to life as Leipzig coach continued with a third straight win to kick off the league season.
Leipzig, who were drawn in Champions League Group G alongside Zenit Saint-Petersburg, Benfica and Lyon on Thursday, had beaten Union Berlin and Eintracht Frankfurt in their first two games.
They continued their strong form as Werner latched onto Emil Forsberg's through ball to slip a shot between the legs of Gladbach goalkeeper Yann Sommer and give the visitors a 38th-minute lead at Borussia Park.
Leipzig caught their hosts cold less than two minutes into the second period, as Yussuf Poulsen sent Werner racing in on goal again, and the 23-year-old made no mistake.
He made it five goals in just three league appearances in the final minute of added time after Breel Embolo had briefly given the home fans some hope, slotting calmly into the bottom corner.
A first defeat of the season leaves Gladbach seventh on four points.
Last season's runners-up Borussia Dortmund will have an opportunity to retake top spot when they visit promoted Union Berlin on Saturday, while reigning champions Bayern Munich host Mainz.