Luca Antonini bundled the winner home from six yards in the 94th minute and, with just 20 seconds of stoppage time remaining, there was no way back for Massimiliano Allegri's men.
Genoa substitute Alessandro Matri - formerly of Juve - drew the attention of two defenders and cut-back to the unmarked Antonini, who saw his unconvincing shot hit the back of the net despite the best efforts of the desperate visitors.
It was a cruel way for Buffon's milestone match to end as a tired Juve lost just their second league match of 2014.
Juve were twice denied by the woodwork on Wednesday, with Fernando Llorente firing into the base of the left post midway through the first half.
Defender Angelo Ogbonna lifted over Genoa goalkeeper Mattia Perin in the 70th minute, but saw his effort hit the post after the hosts were caught napping at the back.
And those close-calls came back to haunt Juve - playing their fourth match in 12 days - as Antonini netted a dramatic winner.
Juventus remain top of the league, but second-placed Roma beat Cesena to join them on 22 points.
Buffon wore a special captain's armband that simply read '500' for a Juventus side who brought in Paul Pogba and Stephan Lichtsteiner, while Matri started on the bench for the hosts - despite scoring in their 2-1 win at Chievo on Sunday.
After a slow start, Juve - controlling possession - finally turned the screw in the 22nd minute, as Carlos Tevez cut inside and forced a good low save from Perin when he tried to fire into the bottom-right corner.
Llorente was next to go close, but shot into the woodwork after showing good control to shield an opponent.
Tevez and Pogba shot wide from distance as half-time approached and the off-target efforts continued after the break - Lichtsteiner and Leonardo Bonucci the latest culprits.
Buffon made his first save of the night in the 64th minute, tipping a swerving Giovanni Marchese effort over the bar, while at the other end, substitute Alvaro Morata played in Tevez - only for him to smash over from 20 yards.
Ogbonna then had his near miss after he reacted quickest to a header back into the box, only to see his effort come back off the post.
Morata forced a tidy stop from Perin from an acute angle in the 84th minute, and the goalkeeper went one better as the final whistle approached, reacting quickly to excellently tip another effort from the Spaniard over.
And Perin's saves proved crucial as Antonini's first league goal of the season gave Genoa a famous win.
