The Argentina striker found the back of the net once in each half to take his league tally to 101 and consign Milan to a fourth consecutive home game in all competitions without a victory.
If a miserable run at San Siro does not do for head coach Montella, it may be the Rossoneri's poor record against top-six sides this season that costs him his job - Juve followed Lazio, Roma and Inter Milan in making light work of big-spending Milan.
While this was not a particularly poor Milan performance, they were listless in attack and their forwards' failings were only emphasised by the presence of Higuain in the opposing ranks.
The 29-year-old thrashed a ruthless effort into the net after 23 minutes and then doubled his tally shortly after the hour-mark with a similarly devastating strike, suggesting he is returning to his prolific best after a difficult start to the campaign.
Milan could slip into the bottom half this weekend as a result, while reigning champions Juve moved level at the summit with Napoli, who host Sassuolo later this weekend.
Clearly aware of the enormity of the fixture and their desperate need for a result, Milan started at a great pace at a baying San Siro.
Gianluigi Buffon punched an early Ricardo Rodriguez free-kick away from his near post and Nikola Kalinic should have turned a shot on target amid a chaotic goalmouth scramble.
But as the blood and thunder of the opening 10 minutes faded, Juve gained a foothold and the dangerous Paulo Dybala tested Gianluigi Donnarumma from range before Higuain broke the deadlock.
Dybala fed a pass into his strike partner, who controlled instantly and snapped a finish inside the right-hand post for his landmark strike.
The Bianconeri retreated into their shell, but Milan lacked the cutting edge to make the most of a dominant end to the first half and Kalinic passed up their biggest chance as he rattled the crossbar from close range.
Milan's momentum slowed again after a bright spell after the restart and they were grateful to twice see Dybala miscue in positions he has readily scored from in the past.
But Higuain would not miss. Dybala dummied Kwadwo Asamoah's pass to give the former Napoli man time and space to steady himself and fire home via the base of the post.
Juve assumed complete control throughout the closing stages, with Higuain and Dybala continuing to combine but sparing Milan the humiliation of a third as Montella's men crumbled again.
Key Opta stats:
- Gonzalo Higuain has now scored 101 goals in 153 appearances in Serie A.
- Over the last 20 seasons, Higuain is only the second player to score over 100 goals in two of the top-five European leagues - the first was Zlatan Ibrahimovic.
- Juventus have won nine of their last 10 Serie A matches against AC Milan (one defeat).
- AC Milan have failed to score in their last three home league matches – their longest goal scoring drought at home in Serie A since December 2007.