كتب : Hatem Maher
Dutch international striker Roy Makaay had the opener three minutes before the break before Fabio Junior's effort brought Bochum level in the 52nd minute.
But German international full back Philipp Lahm secured the three points for the German champions five minutes after the hour mark.
Bayern are in third place of the Bundesliga table with six points, behind Nurnberg and Bremen who lead on goal difference.
Elsewhere, nine-man Stuttgart grabbed a hard-fought 3-2 away victory over Arminia Bielefeld.
Fernando Meira gave Stuttgart the lead in the 39th minute before Abdelaziz Ahanfouf leveled the score from the penalty spot in the 66th minute as Ricardo Osorio was sent off for handling the ball inside the area.
Antonio Da Silva restored the lead for Stuttgart in the 73rd minute but Jorg Bohme equalized three minutes later.
Although Da Silva received his marching orders ten minutes from time, Brazilian striker Cacau grabbed the winner for Stuttgart in the 82nd minute.