Substitute Alvaro Morata lit up a lacklustre performance from the Serie A leaders at Stadio Renzo Barbera with a superb curling effort in the 70th minute.
That proved enough for champions Juve to stretch their lead over second-placed Roma, who do not play until Monday, to 14 points and head coach Allegri praised a job well done against a Palermo side who had not lost their previous 10 home games.
"It wasn't an easy game," Allegri told Sky Sport Italia. "The boys showed a sign of maturity.
"We could have done better after going up 1-0, but it's an achievement that we take another win on the way to the Scudetto."
Juve now turn their focus to Wednesday's UEFA Champions League last 16 second leg tie at Borussia Dortmund.
Allegri's men hold a 2-1 lead from the first encounter in Turin and he is sure his players are in the right frame of mind to progress to the quarter-finals.
"We know Borussia's qualities, but it is also a game where we need to score at least one goal, probably two," he added.
"That means a lot of balance, being in the match and having a bit of luck too.
"We have the right enthusiasm to face this challenge, seeing as we are so far ahead in Serie A."
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