Juve moved second and level on points with Lazio after Milos Krasic's effort from a narrow angle went in off goalkeeper Fernando Muslera deep into stoppage-time.
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"This is a big step forward," Chiellini, whose coach Luigi Del Neri played for veteran Lazio boss Edy Reja way back in 1984 with Gorizia, told Sky. "We know how to suffer and then strike. To score right at the end was great."
Fellow promoted side Lecce also picked up a 3-2 victory over Chievo but stayed third-from-bottom while Brazilian striker Nene netted a hat-trick in Cagliari's 3-0 win over nine-man Catania.
Milan's easy victory meant they moved 13 points ahead of faltering rivals Inter in seventh, who are not playing this weekend because of their involvement in the Club World Cup.
The Rossoneri, who had already qualified for the last 16, suffered a wobble in Wednesday's home Champions League defeat by Ajax Amsterdam but Zlatan Ibrahimovic returned to the team in place of Ronaldinho at Bologna and his extra spark was key.
Ibrahimovic then chested down and finished off Andrea Pirlo's pass in the second half, meaning Milan's three main close-season signings all scored again for the second straight league game following last weekend's 3-0 win over Brescia.
Bologna's players have not been paid for weeks and the club has been put up for sale with the first team able to walk out for free in January if wages are still not forthcoming.
