The Argentina striker provided a textbook finish in the 17th minute to put Juve ahead and cleverly assisted Federico Bernardeschi to double the hosts' just after the hour.
Coach Maurizio Sarri will have been delighted to see such an effective performance from Higuain, a player who was much maligned during a difficult 2018-19 campaign. Although Juve rarely shifted through the gears, a fine outing was completed by Cristiano Ronaldo netting the third goal late on.
A win for Juve means they and Atletico Madrid each have four points from two Group D games and the Bianconeri can switch their focus to a domestic showdown with unbeaten Serie A rivals Inter on Sunday.
There was little goal threat from either side until Higuain opened the scoring in fine fashion.
Jonathan Tah failed to properly deal with Juan Cuadrado's forward punt and Higuain took a brilliant first touch before rifling low into the left corner from 20 yards.
Lukas Hradecky denied Higuain a second goal with a smart parry from the striker's bending effort from the left of the penalty area.
Ronaldo was largely quiet until a Cuadrado pass found its way to the Portugal star in the 57th minute, but he uncharacteristically shot straight at Hradecky.
Juve were celebrating again shortly after, however, as Higuain showed great feet and his centre was swept home by Bernardeschi.
Higuain should have had another assist when his low left-wing ball found a wide-open Ronaldo who again could only drill an effort against Hradecky.
It was a case of third time lucky, though, when Ronaldo drilled through Hradecky's legs after being teed up by Paulo Dybala to score against a 33rd different team in the Champions League - tying Raul's record - to round out the win.
What does it mean? Juve well on track
Juve will have been disappointed at surrendering a two-goal lead to draw their opener at Atletico, but ultimately a point at the Wanda Metropolitano is a good result. After overcoming a potentially tricky home fixture here, Sarri's side are well placed for a last-16 berth.
That's the Higuain we know and love
Higuain endured disappointing loan spells at AC Milan and Chelsea – the latter under Sarri – last season. But he has been a regular starter this term back at Juventus and his goal was reminiscent of Higuain at his best - the touch to set his strike was a thing of beauty. More good work set up Bernardeschi for Juve's second and Higuain's contributions were vital to Juve's win.
Tah error undoes Leverkusen game plan
Leverkusen had a pretty solid game plan: keep the ball, try and coax Juventus out to play, then hit the hosts on the transitions. Unfortunately, Tah's undercooked header from Cuadrado's lump in the air presented the platform for Higuain's brilliance and left his team chasing the game.
Juventus return to Serie A action in a mouth-watering table-topping clash against Inter in the Derby D'Italia on Sunday. Leverkusen host RB Leipzig in the Bundesliga a day earlier.