Kiessling, battling to reclaim a spot in the Germany team, moved joint top of the scorers' list with a 37th minute effort after fine work from Germany international Andre Schuerrle.
In-form Leverkusen's sixth win in their last seven games lifted them to 30 points.
Schalke 04, who face Montpellier in the Champions League next week, are now without a win in their last four Bundesliga matches after salvaging a 1-1 draw at home to Borussia Moenchengladbach with a late equaliser.
Julian Draxler's 86th minute goal cancelled out Igor De Camargo's fine strike on the hour to leave Schalke fourth on 25 points.
Ten-man Mainz 05 left it even later in their 2-1 victory against Hanover 96 with Adam Szalai snatching an 89th minute winner after keeper Christian Wetklo was sent off for a hand ball outside the box.
Mainz, who are sixth on 23 points, moved into European contention with their second win in five days.
VfB Stuttgart are a point behind in seventh after a 1-0 victory at bottom-placed Greuther Fuerth. Shinji Okazaki scored on the rebound after Vedad Ibisevic's spot kick was saved.
Stuttgart were also reduced to 10 men after Serdar Tasci was penalised for a hard challenge early in the second half.