Juventus boss Massimiliano Allegri praised his side for learning from their defeat to Manchester United and responding with a 2-0 victory over AC Milan on Sunday evening.
The Italian side suffered a 2-1 loss against United in the Champions League on Wednesday, but appeared to have put it behind them as they took on their Serie A rivals.
Mario Mandzukic led the way with his fifth goal of the season before Cristiano Ronaldo added a second late on to restore Juve's six-point advantage at the top of the Serie A table.
Allegri described the result as a "big step forward".
Quoted on the Juventus website, he said: "Losing against Manchester United has done us good and tonight it was a good response from the team.
"We were a bit shell-shocked by the result on Wednesday but the boys went on the attack straight away in this game.
"We gave away a penalty after a counter attack, which was the only time Alex Sandro and [Blaise] Matuidi both pushed up, but [Wojciech] Szczesny did really well to save.
"This game is a big step forward in the league because we've created a nine-point gap with Inter and we're still six points clear of Napoli."
The game began with a high tempo as both teams pushed for the opener in the early stages.
It took Juventus just eight minutes to break the deadlock as Mandzukic rose high above Ricardo Rodriguez at the back post to head Alex Sandro's pinpoint cross beyond Milan's teenage goalkeeper Gianluigi Donnarumma.
Mandzukic had a chance to score what would have been a carbon-copy goal three minutes later but this time the ball was turned behind for a corner just before it reached him.
Argentina international Higuain, who joined Gennaro Gattuso's Milan on loan from Juve to pave the way for Ronaldo's arrival from Real Madrid, saw a first-half spot-kick saved by Wojciech Szczesny which would have levelled the score before he was dismissed late on.
Juventus flew out of the blocks in the second half, and Ronaldo doubled Juve's lead nine minutes before the end, slamming in the rebound after Joao Cancelo's fierce drive had been parried by Donnarumma.
Allegri added: "In the first half, we perhaps could have organised ourselves better in possession. In the second we did better and we were ruthless from a defensive point of view."
AC Milan manager Gattuso said Juve had shown they had "something more than us both physically and individually".
He told Milan TV: "There are a lot of positive aspects, even if we are doing things halfway right now.
"The team has changed as per character level, they know how to suffer and stay on the pitch.
"But, we lost a bit of vivacity and technique: we must combine both things together."
