Juve lined up in a new 4-2-3-1 formation, which included Mario Mandzukic playing as a winger in a team that also contained Paulo Dybala and Gonzalo Higuain – the first time the attacking trio have played together in Serie A this season.
The system worked a treat, with Dybala and Higuain sending Allegri's men two goals up in Turin within 16 minutes.
Juve held on for a comfortable victory with Gianluigi Buffon having nothing to do aside from two simple saves early in the second half, leaving Allegri pondering using the system again in the future.
"I am not much of a theorist, but every now and then I come up with a mad idea and try it on the pitch," Allegri said to Sky Italia.
"During the week I had not even thought about it, but after a training session the next morning I thought, 'I have to change something'.
"I had said in the press conference on Saturday that it was an option, but nobody expected me to actually do it!
"I don't have to make anyone happy. The important thing is to be sure what you are doing.
"Mandzukic has gone back in time because he played in that role when he was much younger. He also has a never-ending engine and wasn't even tired at full-time. He did very well defending and in terms of technique.
"The system is certainly one option we can use. Everyone was involved and played a great game as a team.
"Even with so many attacking players, we allowed little or nothing to Lazio. We made a few mistakes and could have had many more goals."