Bayern are level with Hoffenheim on 34 points after their 2-1 win over the leaders in Munich on Friday night, but Leverkusen sneaked into third place thanks to their 3-1 win over bottom side Borussia Moenchengladbach on Saturday.
First-half goals by Kiessling put Leverkusen into a 2-0 lead at half-time and they never looked back as his international team-mate Patrick Helmes added a strike early in the second-half.
But 'Gladbach's teenagers managed a consolation goal when Germany midfielder Marko Marin fired in a free-kick which 18-year-old Tony Jantschke, making his Bundesliga debut, headed home to make it 3-1.
"That was an important victory," said Leverkusen boss Bruno Labbadia.
"In the Bundesliga, you have to fight hard against every team you come up against.
"'Gladbach made life hard for us and we had to work hard for every scrap of territory, millimetre by millimetre.
"We did that and we are back in the hunt for the league title now."
Hertha Berlin, who had won their previous three straight Bundesliga games, were beaten 1-0 at Schalke 04 to drop to fourth and yield third to Leverkusen after Gerald Asamoah scored a second-half goal for the Royal Blues.
Greece striker Nikos Liberopoulos scored two first-half goals, equalising with a penalty and added a header to help lift Eintracht Frankfurt up to 11th after their 4-0 win over VfL Bochum.
And two goals in two second-half minutes from midfielder Markus Steinhoefer and defender Marco Russ sealed the rout.
VfB Stuttgart's new coach Markus Babbel has now won his first two games in charge after taking over from Armin Veh as his side strolled to a 3-0 win at Energie Cottbus thanks to an opening first-half goal from Roberto Hilbert.
And Stuttgart's Czech Republic midfielder Jan Simak made the result safe with some ice-cool finishing in the second-half before Sami Khedira also scored to make the result safe at 3-0.
"We began very well and managed to control the game thanks to the early goal," said Babbel.
"But Cottbus got stronger as the game went on and we rode our luck at times.
"The second goal on 63 minutes gave us some security and it settled the nerves."
The defeat leaves Cottbus just above the relegation zone, while Stuttgart are up to eighth.
There was more frustration for struggling Werder Bremen who were beaten 1-0 at Karlsruhe after Stefan Buck fired home off Bremen goalkeeper Tim Wiese in the game's dying stages.
And adding insult to injury in injury time, Bremen were reduced to ten men when former Chelsea striker Claudio Pizarro was shown a straight red for striking his marker Martin Stoll.
The defeat drops Bremen to ninth in the table and is hardly the ideal preparation for the visit of Inter Milan on Tuesday in the Champions League.
Midtable Arminia Bielefeld and Borussia Dortmund took a point each as they ground out a goalless draw.
On Sunday, midtable Cologne host Martin Jol-coached Hamburg who need three points to threaten the leaders while Wolfsburg host Hanover.