Jurgen Ekkelenkamp scored Hertha's late consolation.
"It was fun, we controlled the game for the whole 90 minutes," said Bayern's Joshua Kimmich, who returned to midfield having played the two previous games at right-back.
Kimmich, who set up goals for Mueller and Gnabry, revealed Bayern striker Robert Lewandowski, the league's top-scorer, was annoyed that he failed to add to his tally of 23 goals.
"We teased him about that," Kimmich said.
A third straight home defeat capped a miserable week for Hertha who were knocked out of the German Cup on Wednesday by a 3-2 derby loss to Union Berlin.
After Dortmund had trimmed Bayern's lead in the table with a 3-2 win at Hoffenheim on Saturday, Bayern had few problems restoring their commanding lead in the table.
Tolisso backed up last weekend's goal at Cologne with a superb diving header after a cross from fellow Frenchman Kingsley Coman.
Mueller then tapped in a Joshua Kimmich free kick when he ghosted behind the defence and rolled the ball past frustrated Hertha goalkeeper Alexander Schwolow.
The Berlin shot-stopper had kept his side in the game with 12 saves up until that point, but his luck deserted him when a pass out to Hertha defender Linus Gechter was intercepted by Sane who tucked the ball into an empty net.
Gnabry fired in the fourth.
Hertha restored some pride with a late consolation when replacement Jurgen Ekkelenkamp profited after a mistake by Bayern defender Dayot Upamecano, who had just come on, to score.
Sane was only denied a superb second goal after VAR spotted he controlled the ball with his shoulder before unleashing a long-rang shot.
Earlier, RB Leipzig defender Josko Gvardiol marked his 20th birthday with a late goal to seal a 2-0 home win over Wolfsburg, who have now gone nine Bundesliga games without a win.
Croatia defender Gvardiol tapped in a late effort which was initially flagged offside before the VAR confirmed the goal after centre-back Willi Orban headed Leipzig into the lead 14 minutes from time.
Leipzig have won their last four games in all competitions and are back up to sixth in the table.
The latest away defeat ramps up the pressure on Wolfsburg head coach Florian Kohfeldt, who only replaced his sacked predecessor Mark van Bommel in late October.
"We want to get through this phase together," said Wolfsburg sports director Marcel Schaefer, who confirmed Kohfeldt will be in charge for their next match against bottom side Greuther Fuerth.
Wolfsburg wasted a golden double chance just before half-time when Leipzig goalkeeper Peter Gulacsi denied Belgian midfielder Aster Vranckx at close range, then Konrad Laimer just managed to block Yannick Gerhardt's shot.
In a bid to force the opening goal, Leipzig coach Domenico Tedesco made a triple substitution early in the second half by bringing on Tyler Adams, Lukas Klostermann and Dani Olmo.
The switch paid off as Olmo's chip was headed off the post by Andre Silva before defender Orban pounced on the rebound to put the hosts ahead 14 minutes from time.
Wolfsburg's defence buckled again eight minutes later when Silva put Nordi Mukiele away and the Frenchman slipped the ball to the unmarked Gvardiol to hit the net.