Federico Peluso's 94th-minute winner for Sassuolo, which came minutes after his team missed a penalty, meant bottom team Benevento were condemned to a record-extending 13th straight Serie A defeat.
Juve trailed 3-0 at Sampdoria before stoppage-time goals by Gonzalo Higuain, with a penalty, and Paulo Dybala made the score more respectable.
Juventus rested goalkeeper Gianluigi Buffon and defender Andrea Barzagli, who both confirmed their international retirements after playing in Monday's 0-0 draw with Sweden which meant Italy failed to qualify for next year's World Cup.
They missed a host of first-half chances then collapsed after the break as Samp maintained their perfect home record.
Duvan Zapata headed Sampdoria ahead in the 52nd minute, Lucas Torreira blasted the second and Gian Marco Ferrari turned in Fabio Quagliarella's cross from the byline for the third.
"It was one of our best first halves of the season and we just needed to keep our cool in front of goal," said Juve coach Massimiliano Allegri. "They scored three goals from four shots."
Icardi put Inter ahead in the 52nd minute against Atalanta when he got away from his marker to head in Antonio Candreva's free kick and struck again with a superb glancing header from Danilo D’Ambrosio's cross on the hour.
Napoli, 2-1 winners over visiting AC Milan on Saturday, lead the standings with 35 points from 13 games ahead of Inter on 33, with both teams still unbeaten. They are followed by Juventus on 31, AS Roma on 30 and Lazio with 28.
"GOOD EFFORT"
Benevento gifted Sassuolo the lead after 57 minutes when Alessandro Matri was left to tap the ball into an empty net after a backpass was intercepted by Simone Missiroli.
In a game that summed up Benevento's season, Samuel Armenteros equalised eight minutes later but they almost immediately had Gaetano Letizia sent off for a second booking.
Benevento held out until added time when Sassuolo got a penalty for handball which Domenico Berardi smashed against the bar.
The home team's relief was short-lived, however, as Peluso headed in from a corner for the winner from the next attack, the second time Benevento have been beaten deep into stoppage time.
“We put in a good effort and the attitude is there," said Benevento coach Roberto De Zerbi. "It's our fault that we lost points again at the end - in those situations, the ball has to be cleared."
In other matches, Luca Rigoni's early goal gave Genoa a 1-0 win at Crotone and a winning start to Davide Ballardini's third stint as their coach after he replaced Ivan Juric.
Torino striker Andrea Belotti had a second-half penalty saved by Stefano Sorrentino as the Bulls were held 1-1 at home by Chievo, while Fiorentina's match at SPAL ended with the same scoreline and Cagliari won 1-0 at troubled Udinese.
(Writing by Brian Homewood in Bern; Editing by Toby Davis and Ken Ferris)
