Bayern beat Hoffenheim 2-0
Bayern provisionally lead the standings on 36 points with Bayer Leverkusen, who slip to second a point behind, hosting Mainz on Saturday.
Schalke 04, with 34, host lowly Nuremberg on Sunday on the first weekend back from the winter break.
Klose sealed Bayern's victory in the 86th minute with his first goal of the season when he tapped home from close range after defender Demichelis had given them the lead with a volley in the 35th before a capacity crowd at the Allianz Arena.
The hosts picked up where they left off before the seasonal break, notching their seventh straight win in all competitions and enjoying their 11th league game undefeated.
Hoffenheim goalkeeper Timo Hildebrand was in sparkling form, denying the hosts on a dozen occasions as the Bavarians stampeded past the visitors' defence in the second half.
"We hoped to spread fear and I think we did it," Bayern coach Louis van Gaal told reporters. "I think our (title) rivals saw tonight that we have a good team."
"We did not play well in the first half but in the second we did it really well and created great chances," said the Dutchman.
The away side initially took control and threatened twice in the opening minutes through Demba Ba's close range effort and Argentine midfielder Franco Zuculini's shot from distance.
However, a Bayern's compact central defence and winger Arjen Robben's pace soon began to wear down a Hoffenheim midfield badly missing injured playmaker Carlos Eduardo.
Demichelis grabbed the lead after Hoffenheim's Josip Simunic failed to clear a Bastian Schweinsteiger cross, heading the ball into the path of the Argentine defender.
Bayern's Mario Gomez squandered a golden opportunity to double their lead in the 57th when he was sent through by Robben but a poor first touch allowed Hildebrand to save.
The Germany striker then failed to beat the keeper with a close-range header as Bayern launched waves of attacks.
The former Germany international denied Robben and Thomas Mueller before Klose connected with a Mark van Bommel cross four minutes from time to end his Bundesliga goal drought.
Gomez's bad luck on the night was summed up when he hit the post in stoppage time.