Germany striker Werner, who returned to Leipzig this week after two years at Chelsea, fired a dipping shot from outside the box at Cologne keeper Marvin Schwaebe, who let it slip through his hands to gift Leipzig the opener in the 36th minute.
The hosts, who drew 1-1 against VfB Stuttgart last week and also lost to Bayern Munich in the German Super Cup had earlier put the ball in the net twice only for their efforts to be over-ruled by VAR.
Leipzig's lead was short-lived, with Florian Dietz sliding in to stab the ball home for the equaliser four minutes later after catching the Leipzig defence napping.
Christopher Nkunku, Bundesliga's player of the season in the previous campaign, took matters into his own hands in the 56th and put the hosts in front with a fine finish after a run into the box.
But Cologne bounced back once more courtesy of Leipzig's Josko Gvardiol's own goal in the 72nd after he turned a corner into his own net.