Palermo saw their 2-0 lead cancelled out by an Alessandro Del Piero brace in the second half and he also hit the woodwork, but Mattia Cassani's screamer in the final minute sealed the scoreline.
"If I have to analyse this game, then I say Palermo had three shots on goal and Gigi Buffon did not make a single save," insisted Ranieri. "We took a while to get into gear, but Amauri's goals did not knock us down. After the break I think nobody could complain if we were 4-2 up.
"It was heading towards a draw and even that seemed to be limiting considering what we'd done, but this is football. We never give up and towards the end pinned the Rosanero back into their own half."
Momo Sissoko was particularly impressive in midfield and had a hand in both Bianconeri goals.
"He settled in immediately, feels like one of the team and is eager to work hard. He has character and can still grow."
Ironically, Juventus President Giovanni Cobolli Gigli confirmed his interest in signing Amauri before this game.
"He could have found other ways to convince us!" joked Ranieri.
Palermo boss Stefano Colantuono also concedes that his team was lucky to emerge with all three points - their first win in six.
"In the second half we struggled under the sheer physicality of Juve's game and risked compromising the whole result. Having said that, we dominated the first half.
"We also had problems because we lost Roberto Guana and Fabio Simplicio to injury and their replacements have different characteristics.
"This victory allows us to escape from the negative cycle and we are ready for the derby against Catania."