The Rossoneri, chasing a first scudetto since 2004, moved three points clear at the top having been briefly caught on Friday by Lazio who beat troubled champions Inter Milan 3-1.
Sixth-placed Inter are now 10 points behind city rivals Milan and their chances of a sixth straight title look remote after 15 games of the season.
Midfielder Kevin Prince Boateng netted his first league goal for the club in the fourth minute after Ibrahimovic's assist.
The softly-spoken manager has shown his tougher side by daring to leave the underperforming Ronaldinho out despite the playmaker being club owner Silvio Berlusconi's favourite.
The result, along with limiting Andrea Pirlo's slowing influence on the side, has been a quicker and more incisive Milan than the versions seen in the last five years.
"It's important to carry on like this, often it's happened and it will happen that someone is left out. The key thing is that those who play give their all," Allegri told Sky.
"Tonight we can be happy but the championship is still long. Last season (runners-up) Roma made up 14 points on Inter."
Davide Moscardelli sparked Chievo's comeback midway through the second half before Pablo Granoche equalised seven minutes from time and Roma's Daniele De Rossi was sent off for a foul.
Ranieri rested forwards Marco Borriello and Francesco Totti after last weekend's 3-1 defeat at Palermo and with one eye on next week's crucial Champions League group match at CFR Cluj.
Next weekend's games are threatened by a players' strike.
