Alessio Romagnoli dispatched a dramatic 97th-minute winner at Dacia Arena in a repeat of the stoppage-time heroics that earned Milan a 2-1 win over Genoa in midweek.
The captain's composed finish amid a frantic finale made it three wins from three since the derby heartbreak against Inter, which remains fresh in Gattuso's mind ahead of next weekend's meeting Juventus.
Higuain is in doubt to face his parent club after a collision with Rolando Mondragora forced him off just 35 minutes into the hard-earned triumph against Udinese.
"He felt a twinge in his back," Gattuso said of the striker. "He had problems with it when he was younger and underwent surgery years ago.
"Hopefully it's nothing serious.
"We faced a very physical team but we were much better in the second half and deserved the win today. I know what's it like to lose in the last minute, it happened to us in the derby.
"We won without a lot of injured players. Now we have to try to regain our energy and get a few players back."
Gattuso was dismissed from the touchline during the late confusion which erupted around Romagnoli's winner.
VAR was required to correct an erroneous offside flag which had threatened to spoil Milan's moment, but the Rossoneri boss took no issue with the officiating.
"I didn't say anything, I was expelled for leaving my technical area," he said.
"It was the right decision."