A seventh consecutive home Champions League defeat for the Scottish champions equals the competition record and leaves Celtic rooted to the foot of their group with just one point from four games.
Leipzig's first away win in Europe, or the Bundesliga, since April puts them in the driving seat to reach the last 16.
Marco Rose's men move above Shakhtar Donetsk into second place in the group after the Ukrainians were denied a shock win by a 96th minute equaliser for Real Madrid in a 1-1 draw in Warsaw.
Celtic trail Shakhtar by four points and need to win when the sides meet in two weeks to have any chance of even salvaging Europa League football in the new year.
It was a familiar story for Celtic as a failure to take their chances came back to haunt Ange Postecoglou's men.
Daizen Maeda's header flew inches wide of the far post inside the first minute, while Matt O'Riley and Greg Taylor saw shots come back off the woodwork in the first half.
Kyogo Furuhashi also headed over a glorious chance with the score at 0-0.
However, Leipzig were deserving winners on the night as their greater quality told the longer the game went on as Celtic struggled without captain Callum McGregor and one of their major threats Jota through injury.
Joe Hart was the villain for the Hoops when the sides met in Germany last week as his errant pass handed Andre Silva the decisive goal in a 3-1 Leipzig win.
The former England number one went some way to redeeming himself with a stunning save with his right foot to turn Christopher Nkunku's strike over just before half-time.
Hart made another big stop to deny Willi Orban at the start of the second period.
Nkunku just failed to get a strong enough connection on a near post header and had a penalty appeal turned down after Hart raced off his line as Leipzig ramped up the pressure.
And it eventually told when Werner cushioned home Andre Silva's cross into the far corner.
Celtic still had their chances to snatch a point as O'Riley stung the palms of Janis Blaswich and Giorgos Giakoumakis' somehow failed to hit the target with a header at the back post.
But any hope of a revival from the hosts was extinguished six minutes from time when Forsberg controlled Werner's pass and slotted into the top corner.
