The reigning Serie A champion moved a provisional six points clear at the top of the table with the result, ahead of second-placed Roma's big clash against Fiorentina on Sunday.
And Chiellini, who scored the second goal of the game at the death after Arturo Vidal's opener, explained that his side were focused solely on getting three points right from the first whistle.
"We started off really well, and showed from the offset that we wanted to win," he said to Sky Sport Italia.
"It was a difficult game today. Bologna have the likes of [Alessandro] Diamanti, so we knew that they would be dangerous.
"But we wanted to win at all costs, and we did."
Juve’s next match is a crucial trip to Istanbul to face Galatasaray in the Champions League, with the Bianconeri needing to avoid defeat to assure themselves of a spot in the knockout stages.