A single Simone Zaza strike in the closing stages of the game was enough for the reigning champions to clinch a vital three points in Turin and leapfrog the Partenopei into first place.
And although Allegri has warned his players that they cannot afford to get carried away, he feels their 15th consecutive league victory shows they deserve to be at the top of the table.
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"It was a very tactical game between two teams that deserve to be at the top of the table," Allegri said at a media conference.
"Napoli put in a great performance, but we hardly gave away any chances. We got a good chance with Paulo Dybala and eventually got the goal. We coped well with Napoli's pace.
"It wasn't easy to win. It's important to have gone top of the table, but there are still 13 games to go.
"We sit top of the table because we have won 15 games in a row. The players deserve all the credit for it. It was a big test for us.
"We had to show that we are capable of winning the league and the lads did very well. There are still a lot of games to go, but this is an important win psychologically.
"We knew they could hurt us if we gave them too much space, but we gave very little away. The team has grown a lot. The players never stopped believing in our title chances.
"Our belief has really grown and the younger players have made steps forward."
Juventus hold a one-point lead over Napoli following Saturday's victory and resume Serie A action on Friday when they travel to Bologna.