The Argentine midfielder scored one goal and set up the other two to send Napoli up to joint fifth, two points behind Milan who are fourth after leapfrogging Parma thanks to Marco Borriello's double in a 2-0 home win.
"When a coach makes a change... it's so the players will respond and Datolo has done really well," Napoli boss Walter Mazzarri, who has won three out of four games since replacing Roberto Donadoni at the start of the month, told Sky television.
Juve, second in the table, came into the game on a high after Wednesday's 5-1 thrashing of Sampdoria but left the pitch completely stunned having appeared to have the match wrapped up.
He scrambled home the equaliser just after the hour mark following Hamsik's corner before his ball into the box led to Slovakia's Hamsik grabbing the winner nine minutes from time.
Substitute Amauri was harshly sent off late on for sliding into Napoli goalkeeper Morgan De Sanctis to complete a miserable second half for Ciro Ferrara's Juve, who fell apart at the back.
"It's difficult to easily analyse the match. Napoli are a side that never give up but it's inexplicable," Ferrara said.
"We take the smack in the face, which hurts, and move on."
Improving Milan, who host Real Madrid in the Champions League on Tuesday when Juve visit Maccabi Haifa, had an early scare when Dida touched Blerim Dzemaili's screamer onto the bar.
The duo combined again in injury time when Borriello acrobatically converted the Brazilian's cross.
