Juve won 2-0 on Sunday thanks to strikes from Paulo Dybala and Higuain inside the first 16 minutes.
It was an impressive response from Massimiliano Allegri's men after they had suffered their fourth league defeat of the season at Fiorentina last time out.
And the former Real Madrid striker was thrilled after a match which saw him score his 12th career Serie A goal against Lazio, making them his favourite top-flight opponents.
"Lazio didn't threaten us in the slightest and we have taken three very big points," Higuain said to Sky Italia.
"The only ones with doubts were the media. We knew full well that we made mistakes, but we had proven ourselves in every other game.
"We figured out what we got wrong at Fiorentina and worked on it."
The victory over fourth-placed Lazio saw Allegri deploy a bold new 4-2-3-1 system, which featured attacking trio Higuain, Dybala and Mario Mandzukic in the same team for the first time in Serie A this season.
"It means we have to work hard but it is an excellent idea," added Higuain, who now has 14 league goals this season.
"It is normal with a more attacking system that we all need to track back and help out in defence, but we proved that we can play like this."
Midfielder Miralem Pjanic was similarly impressed by his team's display, telling Juve's website: "We really enjoyed the system and it was a great response from us.
"We afforded them very little and we were aggressive, creating chances and playing good football. These are three very important points in the title race."