The former Croatia international, who has also coached Eintracht Frankfurt as well as his national side, saw Javi Martinez head in the only goal with just over an hour gone.
Hertha had their chances to score but finished the game with 10 men as Karim Rekik was sent off with six minutes to go.
Davie Selke had seen an early effort disallowed and Salomon Kalou had his shot cleared off the line as the visitors had the better chances in the first half.
Selke also saw his shot cleared off the line early in the second half before Martinez struck to give his side the lead and Bayern held on for the victory.
Hertha had the ball in the Bayern goal after 10 minutes but Selke was flagged offside as he rounded Manuel Neuer before putting the ball into the empty net.
Five minutes later Bayern's Joshua Kimmich hit a shot from the edge of the area which flew narrowly wide of the target.
Just before the half hour, Jerome Boateng cleared off the line when Kalou shot from an acute angle.
Bayern tried to hit back and Franck Ribery saw an effort blocked by Valentino Lazaro but the game was goalless at half-time.
Hertha were again denied by a goalline clearance in the 56th minute as Kimmich got in a block to prevent Selke scoring the opener.
But just after the hour, Bayern opened the scoring when Martinez headed home from a corner by James Rodriguez.
Just 10 minutes after coming on as a substitute, Kingsley Coman, who replaced Ribery, was forced off through injury. Thomas Muller took Coman's place with a little over 20 minutes to go.
Things got worse for Hertha with six minutes remaining as central defender Rekik was shown a straight red card.
The win moved Bayern level on points with Borussia Dortmund who remain top of the Bundesliga on goal difference. The defeat saw Hertha remain in 10th place.