Juve's third defeat of a season in which they are hoping to secure a record sixth consecutive 'scudetto' left the Turin giants just four points ahead of Roma, 3-2 winners over Pescara thanks to an Edin Dzeko brace, and on-form AC, who beat Empoli 4-1 away on Saturday.
Coach Massimiliano Allegri admitted the defeat was a blow in a game that saw Leonardo Bonucci and Dani Alves added to the club's lengthy injury list, Alves notably suffering a fractured shin that could rule him out for several months.
"It's a blow and has brought us back to earth with a bump," said Allegri of the champions' third defeat of the campaign.
"I'm angry, but no team is capable of winning all the time."
Juventus travelled to the Luigi Ferraris Stadium without a number of key players, with forwards Paulo Dybala and Marko Pjaca and defender Andrea Barzagli notably all in the treatment room.
Experienced defender Giorgio Chiellini was only fit enoug for the bench, meaning a start in the back three for Swiss wing-back Stephan Lichtsteiner.
With Argentine striker Gonzalo Higuain in the same straits due to a muscle problem, Allegri was forced to play Juan Cuadrado up front alongside Mario Mandzukic.
Genoa sensed an upset, and were 2-0 up by the 13th minute thanks to a fine Simeone double.
"We're delighted to have beaten the strongest team in Italy, it gives you a special kind of satisfaction," said Genoa coach Ivan Juric.
"We had a great game and everyone was completely focused. I want us to kick on from this and have more confidence in ourselves."
For the opener, Lichtsteiner was outfoxed by Diego Laxalt in midfield and the fleet-footed Uruguayan motored away to set up Luca Rigoni for a drive that Gianluigi Buffon did well to parry.
Lucas Ocampos was quick to the rebound and when Buffon stopped the ball again, Simeone pounced to beat the keeper at the second time of asking.
When Simeone was left unmarked on the edge of the box the 21-year-old Argentine ran in to direct a diving header past Buffon from Darko Lazovic's pinpoint delivery.
A nervous Juve conceded a third before the half-hour when Rigoni's volley from a chaotic corner was hit past Buffon and into the net by Alex Sandro for an own goal.
Juve avoided a total whitewash when Miralem Pjanic stepped up to curl a superb free-kick past Mattia Perin eight minutes from the end.
Atalanta win again
Elsewhere Crotone moved off bottom spot thanks to a 1-1 home draw with Sampdoria, thanks also to Palermo's earlier 1-0 defeat to Lazio that sent the Sicilians to rock bottom.
Lazio are up to third, just five points behind Juve, ahead of next week's derby with Roma.
Coach Simone Inzaghi said thoughts of a derby win had inspired them on their way to a dominant, 1-0 win provided by Sergej Milinkovic-savic's 31st minute winner.
"It had an effect on us, for sure," he said. "Our fans expect a lot from us next week so we went out to prepare."
Roma raced to a 2-0 lead at the Stadio Olimpico thanks to a Dzeko brace in the space of three minutes that took his league-leading tally to 12, two ahead of Torino's Andrea Belotti and Inter's Mauro Icardi.
But a 60th minute strike from Ledian Memushaj reduced arrears and after Diego Perotti hit a 71st minte third from the spot, Pescara set up a tight, nervous finale after Gianluca Caprari struck their second only three minutes later.
On Monday, Napoli will look to close their nine-point gap to Juve when they host Sassuolo, while Inter Milan host Fiorentina.