The Argentine had failed to score in his last six league outings, but rediscovered his touch as Juve suffered a nightmare opening half an hour during which it conceded three times and left itself too much to do.
Simeone - the son of Atletico Madrid manager Diego Simeone - opened the scoring after just three minutes with a finish from close range, doubling his tally shortly after with a glancing header.
An own goal from Alex Sandro then all but put the match to bed as Genoa claimed its second big scalp of the campaign, having trounced AC Milan 3-0 at home last month.
Miralem Pjanic netted a fine consolation free-kick with eight minutes remaining, but the reigning champion was undone by its dreadful start as it fell to its third league defeat of the season.
This weekend's results see Milan close to within four points of Juve at the summit.
Genoa made a flying start and went 1-0 up after some shocking defending from Leonardo Bonucci sent Luca Rigoni clean through on goal. Gianluigi Buffon did well to deny the winger but the rebound eventually fell to Simeone, who beat the goalkeeper at the second attempt.
Things then went from bad to worse for Juve as Simeone doubled his side's lead with a close-range header from Darko Lazovic's pinpoint cross.
It was all Genoa before the interval and Juve fell 3-0 down before the half-hour mark. Nicolas Burdisso headed the ball into Rigoni's path and the winger steered an attempt against the underside of the bar, before the ball crossed the goalline via the Brazilian's thigh.
There was more bad news for the visitors shortly afterwards when Bonucci was forced off with what seemed like a hamstring injury, Daniele Rugani taking his place in defence.
Juve could have pulled one back early in the second half when Pjanic aimed just wide after being set up by Mario Mandzukic, with Sami Khedira also spurning a gilt-edged chance.
Massimiliano Allegri opted to bring on Gonzalo Higuain for Stephan Lichtsteiner as Juve went looking for a way back in, but their attacking substitution nearly cost them when Simeone popped up in front of Buffon, the goalkeeper only just managing to deflect his shot wide.
To make matters worse for Juve, Dani Alves was forced off injured after they had already made three changes, with Pjanic's magnificent free-kick the only bright spot of an otherwise miserable outing.