Karim Benzema and Gareth Bale netted either side of Higuain's classy curling finish before substitute Borja Mayoral capped off the hosts' third successive pre-season victory in stoppage time.
Mayoral's goal came courtesy of a rebound from Luka Modric's intial effort, the Inter transfer target having returned via the bench for his first 15 minutes of action since the World Cup.
However, Thibaut Courtois - a reported €39million signing from Chelsea in midweek - could miss Wednesday's clash with city rivals Atletico Madrid after sitting out on Saturday, which enabled Keylor Navas to keep his place in goal.
Played as a 60th-anniversary tribute to the European Cup final the two clubs contested in 1958, the match began at a pace befitting that five-goal thriller.
Benzema continued his impressive pre-season by nodding home Dani Carvajal's teasing cross for a second-minute opener.
The lead lasted barely two minutes, though, as former Madrid man Higuain picked out the bottom right corner from 20 yards moments after Navas had denied Fabio Borini.
An end-to-end contest ensued from there with Gianluigi Donnarumma saving from both Bale and Marco Asensio, before a fast-retreating Carvajal cleared a goal-bound Franck Kessie finish off the line.
And there was further drama to come in the first minute of first-half stoppage time, Bale rifling in what proved the winner when a corner dropped kindly in the box.
Gennaro Gattuso gave Mattia Caldara his Rossoneri debut after the interval but there was to be no second equaliser for the Serie A side, who instead shipped a third late on as Mayoral pounced on a loose ball, Donnarumma having saved impressively in a one-on-one with Modric.