Carlos Tevez and Leonardo Bonucci scored first-half goals for leaders Juve, who bounced back after their shock loss to Parma last time out in the league.
Allegri lauded his team for their win over a Lazio outfit that had gone 10 games unbeaten in all competitions heading to Turin.
"I think we have to thank these players because they have played an amazing season. Tonight they played as a great team," he said.
"They know the skills of the opponent and the team conceded a few chances to them. In addition, we took advantage of our chances.
"It wasn't easy to win again the second in the league. This result is really important. We increased the gap to Lazio with seven games left.
"They won eight games in a row conceding only two goals and scoring 19 times."
Allegri has already turned his attentions to the UEFA Champions League, with Juve taking on Monaco on Wednesday while holding a 1-0 lead.
"I still haven’t decided my tactics for Wednesday night," he said.
"It will be a good game from a technical standpoint, but different from the first. We'll need to be at the races."
